FIR Cookbook?
in [DSP]
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From: Jerry Avins on 12 Dec 2006 13:20 jeff227 wrote: >>> So how is it possible to define BW AND the Window? >> By choosing the number of taps to meet the spec. > > > Yes, I know but please read the previous posts - nTaps, Fc, BW, & Window > are ALL input variables to this "Windowed Sinc" coefficient generator. > > My question was what BW does in this routine since "Fc", "nTaps" and > "Window" normally *define* BW. I believe you're right. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: Rune Allnor on 12 Dec 2006 13:22 jeff227 skrev: > >> So how is it possible to define BW AND the Window? > > > >By choosing the number of taps to meet the spec. > > > Yes, I know but please read the previous posts - nTaps, Fc, BW, & Window > are ALL input variables to this "Windowed Sinc" coefficient generator. > > My question was what BW does in this routine since "Fc", "nTaps" and > "Window" normally *define* BW. If BW means "transition bandwith" and nTaps means "number of coefficients", one is obsolete. In my world -- twisted as it admittedly is -- it makes more sense to define the spec in terms of an acceptable transition bandwidth, and from that estimate a number of coefficients that meet the spec, than specifying in advance how many coefficients one wants. Estimating the number of coefficients needed to meet the spec is not difficult; there are clues all over the place. I remember seeing tables for such estimates in the book by Proakis & Manolakis; I would be very surprised if such tables are not present in the book by Oppenheim, Schafer & Buck. Rune
From: Jerry Avins on 12 Dec 2006 13:28 jeff227 wrote: >>> So how is it possible to define BW AND the Window? >> By choosing the number of taps to meet the spec. > > > Yes, I know but please read the previous posts - nTaps, Fc, BW, & Window > are ALL input variables to this "Windowed Sinc" coefficient generator. > > My question was what BW does in this routine since "Fc", "nTaps" and > "Window" normally *define* BW. By the way, bandwidth of these filters in not usually defined by some number of dB down on the skirt as it is with many analog filters. If the passband spec is +/- n dB, the passband is over when the response is out of spec. The filter is characterized by a passband where it meets some spec, a transition band where any response (technically, including a peak) is acceptable, and a stopband with some minimum attenuation. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
From: jeff227 on 12 Dec 2006 17:11 >By the way, bandwidth of these filters in not usually defined by some >number of dB down on the skirt as it is with many analog filters. If the >passband spec is +/- n dB, the passband is over when the response is out >of spec. The filter is characterized by a passband where it meets some >spec, a transition band where any response (technically, including a >peak) is acceptable, and a stopband with some minimum attenuation. > >Jerry Yes, I understand, this is true for many applications. However, I am using these FIR filters in a linear phase, multi-point crossover in an audio application. The reason the -6dB point is significant is because it is the point where, A) HP and LP filter outputs sum to unity and, B) a HP filter can be directly computed by spectral inversion of the LP coefficients. I'm still trying to understand Ron's variables BW, Fc. I have it working but I'm guessing as to what BW and Fc is doing.
From: Ron N. on 12 Dec 2006 17:58
Jerry Avins wrote: > jeff227 wrote: > >>> So how is it possible to define BW AND the Window? > >> By choosing the number of taps to meet the spec. > > > > > > Yes, I know but please read the previous posts - nTaps, Fc, BW, & Window > > are ALL input variables to this "Windowed Sinc" coefficient generator. > > > > My question was what BW does in this routine since "Fc", "nTaps" and > > "Window" normally *define* BW. > > I believe you're right. Not quite. A sinc is the Fourier transform of a rectangle. The width of the frequency response rectangle is the BW parameter, and inversely affects the width of the sinc lobes in the time domain (impulse response). The width of the filter window is almost independent (although there is a minimum width in order to get at least one to three sinc lobes inside the window). The width and choice of window will affect the width of the transition band and the pass and stop band ripple (e.g. the width is the degree to which the filter approximates a rectangle. Infinite width would be a non-windowed sinc with an "infinitely" steep transition. Too narrow a width, and you get a rectangle that looks more like a rounded or triangular filter response.) The center of the rectangle is set by the Fc parameter. 0 for low pass, Fs/2 for high pass. Something in-between for a bandpass. Ron's Q&D FIR filter generator: http://www.nicholson.com/rhn/dsp.html IMHO. YMMV. -- Ron N. |