FirInit Routine

Summary

Initialize a FIR filter.

Declaration

Procedure FirInit(FirTaps: TVec; var FirState: TFirState; UpSample: integer = 1; UpDelay: integer = 0; DownSample: integer = 1; DownDelay: integer = 0);

Description

Initialize the FIR filter by initializing the FirState variable. FirTaps must hold the filter impulse. FirState variable must be initialized with zeros. UpSample and DownSample define the sampling frequency change by an integer factor. UpDelay defines the initial FIR filter delay when upsampling and DownDelay defines the initial FIR filter delay when downsampling. IF Upsample or DownSample are different from 1, a multirate FIR filter is initialized. Multirate FIR filters avoid computing samples which will be discarded, because of the sampling rate change. The multirate filter first performs the upsampling and then the downsampling. Fir filters convolve an impulse response with the signal [1] p. 165:


           M-1
    y[i] = Sum( h[k]*x[i-k] )
           k=0

    x.. input signal.
    h.. impulse response
    y.. output signal

    Convolution can also be written as: y[i] = h[k] ( * ) x[i]
    In frequency domain, convolution becomes multiplication:

    Y[I] = X[I]*H[I]

    Y.. frequency spectrum of the output signal.
    X.. frequency spectrum of the input signal.
    H.. frequency spectrum of the impulse response

Impulse response for typical filter types can be designed with Remez, KaiserImpulse, RemezImpulse and SavGolayImpulse.

See Also
[1] "Understanding digital signal processing, Richard G. Lyons, Prentice Hall, 2001"
FirFilter
FirFree
IirInit
RemezImpulse