SignalUtils.CZT Method

Computes the chirp z-transform.

If the parameters to CZT function do not change between calls, some variables can be pre-computed and stored in to a state variable.

The result is placed in to the Dst variable. The State variable needs to be initialized with a call to CztInit method.

Compute the chirp z-transform.

Compute the chirp z-transform of Src and place it in aResult. The starting frequency is defined with Offset and frequency step is defined with Step. The final frequency is at Offset + k*Step. k defines the number of frequency bins at which to estimated the amplitude and phase of the frequency. Example for computing the Step and Offset:

Step := Expj(-(FStop - FStart)*2*Pi/(k*FS));
Offset := Expj(2*Pi*FStart/FS);

Compute the chirp z-transform.

Compute the chirp z-transform of Src and place it in aResult. The starting frequency is zero and the stop frequency and FStop is at FS/2. k defines the number of steps within that band. RStart is the starting radius of the circle in the z-domain and RStop is the final radius of the circle in the z-domain.

Compute the chirp z-transform over a frequency band.

Evaluates the z-transform of Src at k points spaced equally in angle on a spiral contour in the z-plane, placing the complex result in aResult: X[m] = sum_(n=0)^(N-1) x[n] z_m^(-n), z_m = A W^(-m), m=0,...,k-1. The contour parameters follow directly from the arguments: A = R_(start) e^( j 2pi F_(start)/F_s), W = (R_(stop)/R_(start))^(-1/k) e^(-j 2pi (F_(stop)-F_(start))/(k F_s)). So FStart and FStop are the band edges in the units of the sampling frequency FS, k is the number of output bins across the band, and RStart, RStop set the spiral radius at the first and last bin (use R=1 for the unit circle). With k=N, FStart =0, FStop =F_s the result equals the full DFT of Src.

The algorithm (Bluestein, generalized by Rabiner) costs more than the FFT for the full band but can be cheaper for a narrow zoom band or large zero-padding, and unlike the FFT does not require a power-of-two length. aResult is sized to k complex samples of Src's precision.

References:

[1] Discrete-time signal processing, Oppenheim and Schafer, Prentice-Hall, 1989.

[2] Theory and application of digital signal processing, Lawrence R. Rabiner and Bernard Gold. Prentice-Hall, 1975.