For the better Ordering of selling of Wines by retaile in Tavernes and other places ( (fn. 2) for preventing of Abuses therein Be it Enacted by the Kings most Excellent Majestie by and with the consent of the Lords and Commons in Parliament assembled, and by the Authoritie of the same That noe person or persons whatsoever from and after the five and twentyeth day of March one thousand six hundred sixty one unlesse he or they be authorized and enabled in manner and forme as in this present Act is prescribed and appointed shall sell or utter by retaile that is by the Pint Quart Potle or Gallon, or by any other greater or lesser retaile measure any kinde of wine or wines to be drunke or spent within his or their Mansion house or houses or other place in his or their tenure or occupation, or without such Mansion house or houses or such other place in his or then tenure or occupation by any colour craft or meane whatsoever upon paine to forfeit for every such offence the summe of five pounds the one moyety of every such penalty to be to our Soveraigne Lord the King, the other moyety to him or them that will sue for the same by Action of Debt Bill Plaint or Information in any of the Kings Courts of Record in which Action or Suite noe Essoigne wager of Law or Protection shall be allowed.

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And bee it further Enacted by the Authoritie aforesaid That the Rents Revenues and summes of money hence ariseing, except what shall be allowed for the Wages and Sallaryes of such Officers and Ministers which is not to exceed six pence out of every pound thereof shall be duely and constantly paid and answered into his Majestyes Receipt of Exchequer and shall not be perticularly charged or chargable either before it be paid into the Exchequer or after with any gift or penson, And his Majestyes said Agents are hereby enjoyned and required to returne into the Court of Exchequer every Michaelmas and Easter Termes upon their Oathes (which Oathes the Barons of [the (fn. 3) ] Exchequer or any one of them are hereby authorized to administer) a Booke fairely written containing a true and full account of what Licences have beene granted the preceeding halfe yeare, and what rents and summes of [money (fn. 3) ] are therupon reserved, and have beene paid, or are in arreare together with the securities of the persons soe in arreare to the end due and speedy processe may be made out according to the course of the Exchequer for the recovery of the same

Matlab for Welch's Method Octave and the Matlab Signal Processing Toolbox have a pwelch function. Note that these functions also provide confidence intervals (not covered here). Matlab for generating the data shown in Fig.6.1 (employing Welch's method) appears in Fig.6.2. Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method

Statutes of the Realm: Volume 5, 1625-80. Originally published by Great Britain Record Commission, s.l, 1819.

As usual, the purpose of the window function (Chapter 3) is to reduce side-lobe level in the spectral density estimate, at the expense of frequency resolution, exactly as in the case of sinusoidal spectrum analysis. When using a non-rectangular analysis window, the window hop-size cannot exceed half the frame length without introducing a non-uniform sensitivity to the data over time. In the rectangular window case, we can set and have non-overlapping windows. For Hamming, Hanning, and any other generalized Hamming window, one normally sees for odd-length windows. For the Blackman window, is typical. In general, the hop size is chosen so that the analysis window overlaps and adds to a constant at that hop size. This consideration is explored more fully in Chapter 8. An equivalent parameter used by most matlab implementations is the overlap parameter . Note that the number of blocks averaged in (6.27) increases as decreases. If denotes the total number of signal samples available, then the number of complete blocks available for averaging may be computed as (7.28) where the floor function denotes the largest integer less than or equal to . Matlab for Welch's Method Octave and the Matlab Signal Processing Toolbox have a pwelch function. Note that these functions also provide confidence intervals (not covered here). Matlab for generating the data shown in Fig.6.1 (employing Welch's method) appears in Fig.6.2. Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method

"Charles II, 1660: An Act for the better Ordering the Selling of Wines by Retaile, and for preventing Abuses in the Mingling Corrupting and Vitiating of Wines, and for Setting and Limitting the Prices of the same.". Statutes of the Realm: Volume 5, 1625-80. Ed. John Raithby(s.l, 1819), , British History Online. Web. 24 October 2024. https://www.british-history.ac.uk/statutes-realm/vol5/pp266-268.

Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method

And bee it further Enacted by the Authoritie aforesaid That it shall and may be lawfull to and for his Majestie his Heires and Successors to constitute and appoint such and soe many [other (fn. 3) ] Officers and Ministers as a Receiver Register Clerke Comptroller Messenger or the like for the better carrying on of this service as he and they shall thinke fitt, soe as the Salaries and Wages of all such Officers to be appointed together with the Salary or Wages of his Majestyes said Agents doe not exceed six pence in the pound of the Revenue that shall hence arise.

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And be it further Enacted by the Authoritie aforesaid That such License shall not be given or granted but to such who shall personally use the Trade of selling, or uttering Wines by retaile, or to the Landlord and owner of the House where the person useing such Trade shall sell and utter Wine by retaile, nor shall the same be assignable nor in any wise [beneficiall or (fn. 1) ] extensive to indempnifie any person against the penaltyes of this present Act except the first taker.

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Provided neverthelesse That it shall and may be lawfull to and for the Lord Chauncellour of England, Lord Treasurer, Lord President of the Kings Councell Lord Privy Seale and the two Cheife Justices or Five Fower or three of them, And they are hereby authorized yearely and every yeare betweene the twentyeth day of November and the last day of December and noe other times to sett the Prises of all and every the said Wines to be sold by retaile as aforesaid at higher or lower Rates then are herein contained, soe that they or any of them cause the Prises by them sett to be written, and open Proclamation thereof to be made in the Kings Court of Chauncery yearely in the Terme time, or else in the Citty Burrough or Towne Corporate where any such Wines shall be sold; And that all and every the said Wines shall and may be sold by retaile at such Prises as by them or any Five, Fower or Three of them shall be sett as aforesaid from time to time for the space of one whole yeare to commence from the first day of February next after the setting thereof and noe longer, and noe greater Prises under the paines and penaltyes aforesaid to be recovered as aforesaid, and afterwards, and in default of such setting of Prises by the said Lord Chauncellour of England Lord Treasurer Lord President of the Kings Councell Lord Privy Seale, and the two Cheife Justices or Five Fower or Three or them as aforesaid at the respective Rates and Prises sett by this Actand under the penalties as aforesaid to be recovered as aforesaid.

Provided alwayes and be it Enacted That from and after the First day of September One thousand six hundred sixtie and one noe Canary wines Muskadel or Alegant or other Spanish or sweet Wines shall be sold or uttered by any person or persons within His Majestyes Kingdome of England Dominion of Wales and Towne of Berwicke upon Tweede by retaile for above Eighteene pence the Quart, And that noe Gascogne or French Wines whatsoever shall be sold by retaile above eight pence the Quart, And that noe Rhenish wines whatsoever shall be sold by retaile above Twelve pence the Quart (And according to these Rates for a greater and lesser quantity all and every the said Wines shall and may be sold) upon paine and penalty that every [such (fn. 8) ] person and persons who shall utter or sell any of the said Wines by retaile that is to say by the Pint Quart Potle, or Gallon or [by (fn. 8) ] any other greater or lesser retaile measure at any rate exceeding the rates hereby limitted doe and shall forfeit for every such Pint Quart Potle Gallon or other greater or lesser quantity soe sold by retaile the summe of Five pounds, the one moyetie of which forfeiture shall be to our Soveraigne Lord the King His Heires and Successors and the other moyety to him or them that will sue for the same to be recovered in manner and forme aforesaid.

Provided alsoe That it shall not nor may be lawfull to or for any Officer or Officers to be appointed by His Majestie for the carrying on of this service to take demand or receive any Fees Rewards or summes of money whatsoever for or in respect of this Service other then Five shillings for a License Fower pence for an Acquittance and Six pence for a Bond under the penalty of Ten pounds, one moyety thereof to the Kings Majestie the other moyety to the p[er]son or p[er]sons who shall sue for the same by Action of Debt Bill Plaint or Information wherein noe wager of Law Essoigne or Protection shall be allowed, Any thing herein or any other matter or thing to the contrary notwithstanding

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'Charles II, 1660: An Act for the better Ordering the Selling of Wines by Retaile, and for preventing Abuses in the Mingling Corrupting and Vitiating of Wines, and for Setting and Limitting the Prices of the same.', in Statutes of the Realm: Volume 5, 1625-80, ed. John Raithby( s.l, 1819), British History Online https://www.british-history.ac.uk/statutes-realm/vol5/pp266-268 [accessed 24 October 2024].

Provided alsoe That this Act or any thing therein contained shall not extend or be prejudiciall to the Master Wardens Freemen and Commonalty of the mistery of Vintners of the Citty of London or to any other Citty or Towne Corporate but that they may use and enjoy such Liberties and Priviledges as heretofore they have lawfully used and enjoyed, Any thing herein contained to the contrary notwithstanding.

Provided alsoe and be it Enacted by the Authority aforesaid That this Act or any thing therein contained shall not in any wise extend to debarr or hinder the Maior and Burgesses of the Burrough of Saint Albans in the County of Hertford or their Successors from enjoying useing and exercising of all such Libertyes Powers and Authorities to them heretofore granted by severall Letters Patents under the Great Seale of England by Queene Elizabeth and King James of famous memoryes for the erecting appointing and licensing of three severall Wine Taverns within the Burrough aforesaid for and towards the maintenance of the Free schoole there, but that the same Libertyes Powers and Authorities shall be and are hereby established and confirmed and shall remaine [& continue (fn. 3) ] in and to the said Maior and Burgesses and their Successors to and for the charitable use aforesaid, and according to the tenor of the Letters Patents aforesaid as though this Act had never beene made Any thing herein contained to the contrary in any wise notwithstanding.

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Agents to return into Exchequer, in Michaelmas and Easter Terms, what Licences they have granted, and the Rents reserved.

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And be it further Enacted by the Authoritie aforesaid That it shall and may be lawfull to and for his Majestie his Heires and Successors from time to time to issue out under his or their Great Seale of England one or more Commission or Commissions directed to two or more persons thereby authorizing them to license and give authority to such person and persons as they shall thinke fitt to sell and utter by retaile all and every or any kinde of wine or wines whatsoever to be drunke and spent as well within the house or houses or other place in the tenure or occupation of the party soe Licensed as without in any Citty Towne or other place within the Kingdome of England Dominion of Wales and Towne and Port of Berwicke upon Tweede, and such persons as from time to time or at any time hereafter shall be by such Commission or Commissions as aforesaid in that behalfe appointed shall have power and authority and hereby have power and authority to treat and contract for Licence authority and dispensations to be given and granted to any person or persons for the selling and uttering of Wines by retaile in any Citty Towne or other place as aforesaid according to the rules and directions of this present Act, and the true intent and meaning thereof, and not otherwise, Any Law Statute Usage or Custome to the contrary in any wise notwithstanding.

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'Charles II, 1660: An Act for the better Ordering the Selling of Wines by Retaile, and for preventing Abuses in the Mingling Corrupting and Vitiating of Wines, and for Setting and Limitting the Prices of the same.', in Statutes of the Realm: Volume 5, 1625-80. Edited by John Raithby( s.l, 1819), British History Online, accessed October 24, 2024, https://www.british-history.ac.uk/statutes-realm/vol5/pp266-268.

Persons selling Wines not to mingle the same.; Mingling or abusing Wines.; Penalty £100.; Retailers offending, Penalty £40.

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Provided alwayes That this Act nor any thing therein contained shall not in any wise be prejudiciall to the priviledge of the two Universityes of [the (fn. 4) ] Land or either of them, nor to the Chauncellours or Schollers of the same or their Successors but that they may use and enjoy such priviledges as heretofore they have lawfully used and enjoyed, Any thing herein to the contrary notwithstanding.

Note that the number of blocks averaged in (6.27) increases as decreases. If denotes the total number of signal samples available, then the number of complete blocks available for averaging may be computed as (7.28) where the floor function denotes the largest integer less than or equal to . Matlab for Welch's Method Octave and the Matlab Signal Processing Toolbox have a pwelch function. Note that these functions also provide confidence intervals (not covered here). Matlab for generating the data shown in Fig.6.1 (employing Welch's method) appears in Fig.6.2. Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method

And it is hereby further Enacted by the Authoritie aforesaid That noe Merchant Vintner Wine Cooper or other persons selling or retailing any wine shall mingle or utter any Spanish wine mingled with any French wine or Rinish wine Sider Perry Honey Sugar Sirops of Sugar Molasses or any other Sirops whatsoever, nor putt in any Isinglasse Brimstone Lime Raisins Juce of Raisins Water nor any other Liquor [nor (fn. 5) ] Ingredients, nor any Clary or other Herbe nor any sort of Flesh whatsoever And that noe Merchant Vintner Wine Cooper or other person selling or retailing any Wine shall mingle or utter any French wines mingled with any Rhinish wines or Spanish wines Sider Perry Stummed wine Vitrioll Honey Sugar Sirop of Sugar Molasses or any ( (fn. 6) ) Sirops whatsoever nor put in any Isinglasse Brimstone Lime Raisons Juce of Raisons Water nor any other Liquor or Ingredients nor any Clary or other Herbe nor any sort of Flesh whatsoever, And that noe Merchant Vintner Wine Cooper or other person selling or retailing any Wine shall mingle or utter any Rhinish wine mingled with any French wines or Spanish wines Sider Perry Stummed wine Vitrioll Honey Sugar Sirops of Sugar Molasses [nor (fn. 5) ] any other Sirops whatsoever, nor put in any Isinglasse Brimstone Lime Raisons Juice of Raisons Water nor any other Liquor or Ingredients nor any Clary or other Herbe, nor any sort of Flesh whatsoever, And that all and every person and persons committing any of the offences aforesaid shall incurr the paines and penalties herein after mentioned That is to say Every Merchant Wine-Cooper or other person selling any sort of Wines in grosse mingled or abused as aforesaid shall forfeit and lose for every such offence One hundred pounds, And that every Vintner or other person selling any [sort (fn. 7) ] of Wine by retaile mingled or abused as aforesaid shall forfeite and lose [for every such offence (fn. 3) ] the summe of Forty pounds, of which forfeitures one moyety shall goe unto the Kings Majestie His Heires and Successors the other moyety to the Informer to be recovered in any Court of Record by Action of Debt Bill Plaint or Information wherein noe Essoigne Protection or wager of Law shall be allowed.

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And be it further, Enacted by the Authoritie aforesaid That such persons as shall be commissioned and appointed by his Majestie his Heires or Successors [as aforesaid (fn. 1) ] shall be and be called his Majesties Agents for granting Licenses for the selling and uttering of Wine by retaile, And his Majesties said Agents are hereby authorized and enabled under their Seale of Office, the same to be appointed by his Majestie to grant License for the selling and uttering of Wines by retaile to any person or persons and for any time or terme not exceeding one and twenty yeares if such person or persons shall soe long live and for such yearely rent as they can or shall agree and thinke fitt, soe as noe Fine be taken for the same But that the rent and summes of money agreed upon and reserved be paid and answered halfe yearely by equall portions dureing the whole terme,

When using a non-rectangular analysis window, the window hop-size cannot exceed half the frame length without introducing a non-uniform sensitivity to the data over time. In the rectangular window case, we can set and have non-overlapping windows. For Hamming, Hanning, and any other generalized Hamming window, one normally sees for odd-length windows. For the Blackman window, is typical. In general, the hop size is chosen so that the analysis window overlaps and adds to a constant at that hop size. This consideration is explored more fully in Chapter 8. An equivalent parameter used by most matlab implementations is the overlap parameter . Note that the number of blocks averaged in (6.27) increases as decreases. If denotes the total number of signal samples available, then the number of complete blocks available for averaging may be computed as (7.28) where the floor function denotes the largest integer less than or equal to . Matlab for Welch's Method Octave and the Matlab Signal Processing Toolbox have a pwelch function. Note that these functions also provide confidence intervals (not covered here). Matlab for generating the data shown in Fig.6.1 (employing Welch's method) appears in Fig.6.2. Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method

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Octave and the Matlab Signal Processing Toolbox have a pwelch function. Note that these functions also provide confidence intervals (not covered here). Matlab for generating the data shown in Fig.6.1 (employing Welch's method) appears in Fig.6.2. Figure: Matlab listing for generating data plotted in Fig.6.1.   M = 32; Ks=[1 8 32 128] nkases = length(Ks); for kase = 1:4 K = Ks(kase); N = M*K; Nfft = 2*M; % zero pad for acyclic autocorrelation Sv = zeros(Nfft,1); % PSD "accumulator" for m=1:K v = randn(M,1); % noise sample V = fft(v,Nfft); Vms = abs(V).^2; % same as conj(V) .* V Sv = Sv + Vms; % sum scaled periodograms end Sv = Sv/K; % average of all scaled periodograms rv = ifft(Sv); % Average Bartlett-windowed sample autocor. rvup = [rv(Nfft-M+1:Nfft)',rv(1:M)']; % unpack FFT rvup = rvup/M; % Normalize for no bias at lag 0 end Next Section: Filtered White NoisePrevious Section: Welch's Method