Filter Design Toolbox™

freqrespest - Estimate fixed-point filter frequency response through filtering

Syntax

[h,w] = freqrespest(hd,L) [h,w] = freqrespest(hd,L,param1,value1,param2, value2,...) freqrespest(hd,L,opts)

Description

[h,w] = freqrespest(hd,L) estimates the frequency response of filter hd by filtering a set of input data and then forming the ratio between output data and input data. The test input data comprises sinusoids with uniformly distributed random frequencies.

Use this filter-based technique for judging the performance of fixed-point filters. Because you can compare a filtering-based frequency response estimate for a fixed-point filter to the response of a similar filter that uses quantized coefficients, but applies floating-point arithmetic internally. This comparison determines whether the fixed-point filter performance closely matches the floating-point, quantized coefficients version of the filter.

L is the number of trials to use to compute the estimate. If you do not specify this value, L defaults to 10. More trials generates a more accurate estimate of the response, but require more time to compute the estimate.

h is the estimate of the complex frequency response. w contains the vector of frequencies at which h is estimated.

Refer to example 2 for one way to plot h with w.

[h,w] = freqrespest(hd,L,param1,value1,param2, value2,...) uses parameter value (PV) pairs as input arguments to specify optional parameters for the test. These parameters are the valid PV pairs. Enter the parameter names as string input arguments in single quotation marks. The following table provides valid parameters for [h, w].

Parameter Name	Default Value	Description
`NFFT`	`512`	Number of FFT points to use.
`NormalizedFrequency`	`true`	Indicates whether to use normalized frequency or linear frequency. Values are `true` (use normalized frequency), or `false` (use linear frequency). When you specify `false`, you must supply the sampling frequency `Fs`.
`Fs`	`normalized`	Specifies the sampling frequency when `NormalizedFrequency` is `false`. No default value. You must set `NormalizedFrequency` to `false` before setting a value for `Fs`.
`SpectrumRange`	`half`	Specifies whether to use the whole spectrum or half. `half` is the default, and the valid values are `half` and `whole`.
`CenterDC`	`false`	Specifies whether to set the center of the spectrum to the DC value in the output plot. If you select `true`, both the negative and positive values appear in the plot. If you select `false` DC appears at the origin of the axes.

freqrespest(hd,L,opts) uses an object opts to specify the optional input parameters instead of directly specifying PV pairs as input arguments. Create opts with

opts = freqrespopts(hd);

Because opts is an object, you use set to change the parameter values in opts before you use it with freqrespest. For example, you could specify a new sample rate with

set(opts,'fs',48e3); % Same as opts.fs=48e3

freqrespest can also compute the frequency response of double-precision floating filters that cannot be converted to transfer-function form without introducing significant round off errors which affect the freqz frequency response computation. Examples of these kinds of filters include state-space or lattice filters, in particular high-order filters.

Examples

These examples demonstrate some uses for freqrespest.

Example 1

Start by estimating the frequency response of a fixed-point FIR filter that has filter internals set to full precision.

hd = design(fdesign.lowpass(.4,.5,1,60),'equiripple');
hd.arithmetic = 'fixed';
[h,w] = freqrespest(hd); % This should be about the same as freqz.

Continuing with filter hd, change the value of the filterinternals property to specifyprecision and then specify the word lengths and precision (the fraction lengths) applied to the output from internal addition and multiplication operations. After you set the word and fraction lengths, use freqrespest to compute the frequency response estimate for the fixed-point filter.

hd.filterinternals = 'specifyprecision';
hd.outputwordlength=16;
hd.outputfraclength=15;
hd.productwordlength=16;
hd.productfraclength=15;
hd.accumwordlength=16;
hd.accumfraclength=15;
[h,w] = freqrespest(hd,2);
[h2,w2] = freqz(hd,512);
plot(w/pi,20*log10(abs([h,h2])))
legend('Frequency response estimated by filtering',...
'Freq. response computed by quantizing coefficients only');
xlabel('Normalized Frequency (\times\pi rad/sample)')
ylabel('Magnitude (dB)')

Example 2

freqrespest works with state-space filters as well. This example estimates the frequency response of a state-space filter.

    fs = 315000;
    wp = [320 3800]/(fs/2);
    ws = [50 19000]/(fs/2);
    rp=0.15; rs=60;
    [n,wn]=cheb1ord(wp,ws,rp,rs);
    [a,b,c,d] = cheby1(n,rp,wn);
    hd = dfilt.statespace(a,b,c,d);
    % Compare the following to freqz(hd,8192)
    freqrespest(hd,1,'nfft',8192);

freqrespest - Estimate fixed-point filter frequency response through filtering

Syntax

Description

Examples

See Also