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noisepsd

Power spectral density of filter output due to round-off noise

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Syntax

noisepsdOut = noisepsd(sysobj,L)
noisepsdOut = noisepsd(___,Name=Value)
noisepsdOut = noisepsd(sysobj,L,opts)
noisepsdOut = noisepsd(sysobj,Arithmetic=arithType)
noisepsd(sysobj,___)

Description

noisepsdOut = noisepsd(sysobj,L) computes the power spectral density (PSD) of filter output occurring because of round-off noise. The round-off noise is produced by quantization errors within the filter. The PSD is computed as an average over the L trials.

noisepsdOut = noisepsd(___,Name=Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

noisepsdOut = noisepsd(sysobj,L,opts) uses an options object to specify the optional input parameters in lieu of specifying name-value pairs.

noisepsdOut = noisepsd(sysobj,Arithmetic=arithType) analyzes the filter System object™ based on the arithmetic specified in the arithType input.

example

noisepsd(sysobj,___) with no output argument plots the noise PSD estimate of the filter System object.

Examples

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Open Live Script

Compute the PSD of the output noise caused by the quantization processes in a fixed-point, direct-form FIR filter. The input signal has fixed-point data type. The noisepsd function performs the analysis based on the data type of the locked input.

b = firgr(27,[0 .4 .6 1],[1 1 0 0]);
firfilt = dsp.FIRFilter(Numerator=b) % Create the filter object.
firfilt = 
  dsp.FIRFilter with properties:

            Structure: 'Direct form'
      NumeratorSource: 'Property'
            Numerator: [0.0017 0.0034 -0.0049 -0.0063 0.0094 0.0125 -0.0174 -0.0226 0.0308 0.0409 -0.0576 -0.0846 0.1473 0.4488 0.4488 0.1473 -0.0846 -0.0576 0.0409 0.0308 -0.0226 -0.0174 0.0125 0.0094 -0.0063 -0.0049 0.0034 0.0017]
    InitialConditions: 0

  Use get to show all properties


data = fi(randn(15,16),1,16,3);
output = firfilt(data);

Quantize the filter to fixed-point. Plot the hpsd data. This is the data resulting from the noise PSD calculation. You can review the data in hpsd.data.

hpsd = noisepsd(firfilt,Arithmetic='fixed');
plot(hpsd)

Figure contains an axes object. The axes object with title Power Spectral Density, xlabel Normalized Frequency ( times pi blank rad/sample), ylabel Power/frequency (dB/(rad/sample)) contains an object of type line.

Input Arguments

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Number of trials used to compute the average, specified as a positive integer. The larger you specify L, the more accurate is the estimate of power spectral density but at the expense of longer computation time. When you do not specify L, the function sets L to the default value of 10 trials.

Data Types: single | double

Options object to specify the optional input parameters in lieu of specifying name-value pairs.

Create an opts object with 

opts = noisepsdopts(sysobj);

opts then takes the noisepsd settings from sysobj.

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

set(opts,NormalizedFrequency=false,Fs=48e3);

Arithmetic used in the analysis, specified as 'double', 'single', or 'Fixed'. You cannot use the 'Arithmetic' argument unless you know the data type of the input. If you do not specify the 'Arithmetic' argument, that is, you use the syntax noisepsdOut = noisepsd(sysobj), then the noisepsd function applies these rules:

  • If the System object is Unlocked — The noisepsd function performs double-precision analysis.

  • If the System object is Locked — The noisepsd function performs the analysis based on the data type of the locked input.

If you do specify the Arithmetic argument, that is, you use the syntax noisepsdOut = noisepsd(sysobj,Arithmetic=arithType), the noisepsd function applies these rules depending on the value you set for arithType.

ValueSystem Object StateRule
arithType = 'double'Unlockednoisepsd performs double-precision analysis.
Lockednoisepsd performs double-precision analysis.
arithType = 'single'Unlockednoisepsd performs single-precision analysis.
Lockednoisepsd performs single-precision analysis.
arithType = 'fixed'Unlockednoisepsd produces an error because data type of the fixed-point input is unknown.
LockedWhen the input data type is double or single, then noisepsd produces an error because data type of the fixed-point input is unknown.
When the input data is of fixed-point type, noisepsd performs analysis based on the data type of the locked input.

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: b = firgr(27,[0 .4 .6 1],[1 1 0 0]); firfilt = dsp.FIRFilter(Numerator=b); noisepsdOut = noisepsd(firfilt);

Number of FFT points used in calculating the PSD, specified as a positive integer. This value determines the length of the PSD data vector shown in the Data field of the noisepsdOut structure. When you set NFFT to an:

  • Odd integer –– The length of the PSD data is given by (NFFT+1)/2.

  • Even integer –– The length of the PSD data is given by (NFFT/2)+1.

When not specified, NFFT defaults to 512.

Note

If the spectrum data you specify is calculated over half the Nyquist interval and you do not specify a corresponding frequency vector, the default frequency vector assumes that the number of points in the whole FFT is even. Also, the plot option to convert to a whole or two-sided spectrum assumes the original whole FFT length is even.

Data Types: single | double

Indicate whether to use normalized frequency or linear frequency, specified as either:

  • true –– Use normalized frequency. When not specified, the function defaults to true.

  • false –– Use linear frequency. When you specify false, you must supply the sampling frequency Fs.

Sampling frequency to be specified in Hz when you set NormalizedFrequency to false. When you set NormalizedFrequency to true, Fs is set to 'Normalized'.

Data Types: single | double

Spectrum type of the generated PSD data, specified as:

  • 'Onesided' –– Converts the type to a spectrum that is calculated over half the Nyquist interval. All properties affected by the new frequency range are adjusted automatically.

  • 'Twosided' –– Converts the type to a spectrum that is calculated over the whole Nyquist interval. All properties affected by the new frequency range are adjusted automatically. If you choose a two-sided computation, you can also choose 'CenterDC' as true. Otherwise, 'CenterDC' must be false.

Shift the zero-frequency component to the center of a two-sided spectrum.

  • When you set SpectrumType to 'Onesided', it is changed to 'Twosided' and the data is converted to a two-sided spectrum.

  • Setting 'CenterDC' to false shifts the data and the frequency values in the object so that DC is in the left edge of the spectrum. This operation does not affect the SpectrumType property setting.

Output Arguments

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Data object containing the PSD data, returned as a psd object. To extract the PSD vector from noisepsdOut, enter the following in the MATLAB® command prompt:

get(noisepsdOut,'data')

Plot the PSD data with plot(noisepsdOut). The average power of the output noise (the integral of the PSD) can be computed with avgpower, a method of dspdata objects:

avgpwr = avgpower(hpsd)

References

[1] McClellan, James H., editor. Computer-Based Exercises for Signal Processing Using MATLAB 5. Prentice-Hall, 1998.

Version History

Introduced in R2011a

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See Also

Functions