Display frequency spectrum of time-domain signals

When you choose the Filter Bank method, the Spectrum Analyzer uses an analysis filter bank to estimate the power spectrum.

The filter bank splits the broadband input signal x(n), of sample rate fs, into multiple narrow band signals y0(m), y1(m), … , yM-1(m), of sample rate fs/M.

The variable M represents the number of frequency bands in the filter bank. In the Spectrum Analyzer, M is equal to the number of data points needed to achieve the specified RBW value or 1024, whichever is larger. For more information on the analysis filter bank and its implementation, see the More About and the Algorithm sections in the dsp.Channelizer object.

After the Spectrum Analyzer splits the broadband input signal into multiple narrow bands, it computes the power in each narrow frequency band using the following equation. Each Zi value is the power estimate over that narrow frequency band.

Zi=1L∑m=0L−1|yi[m]|2

L is length of the narrowband signal yi(m) and i = 1, 2, …, M−1.

The power values in all the narrow frequency bands (denoted by Zi) form the Z vector.

Z=[Z0, Z1, Z2,⋯,ZM−1]

The Spectrum Analyzer averages the current Z vector with the previous Z vectors using one of the two moving average methods: video bandwidth or exponential weighting. The output of the averaging operation forms the spectral estimate vector. For details on the two averaging methods, see Averaging Method.

The Spectrum Analyzer uses the value you specify in the RBW (Hz) parameter to determine the input frame length. To view the RBW (Hz) parameter in the scope, click the Analyzer tab on the Spectrum Analyzer toolstrip and navigate to the Bandwidth section.

Spectrum Analyzer requires a minimum number of samples to compute a spectral estimate. This value is directly related to the resolution bandwidth property RBW (Hz).

When you set RBW (Hz) to:

• Auto –– The Spectrum Analyzer requires 1024 samples to update the display. The Spectrum Analyzer determines the appropriate resolution bandwidth to ensure that there are 1024 RBW intervals over the specified frequency span. When you set RBW (Hz) to Auto, the Spectrum Analyzer calculates RBW using this equation.

  RBWauto=span1024

• scalar value –– The Spectrum Analyzer calculates the number of samples Nsamples using this equation.

  Nsamples=FsRBW

  Fs is the sample rate of the input signal as specified in the Sample Rate (Hz) property. To view the Sample Rate (Hz) in the scope, click the Analyzer tab on the Spectrum Analyzer toolstrip and navigate to the Bandwidth section.

  When you specify a resolution bandwidth using the RBW (Hz) parameter, you must specify a value such that there are at least two RBW intervals over the specified frequency span. The ratio of the overall span to RBW must be greater than two.

  spanRBW>2

span is the frequency span over which the Spectrum Analyzer computes and plots the spectrum. To view the Span (Hz) in the scope, click the Estimation tab on the Spectrum Analyzer toolstrip and navigate to the Frequency Options section. To enable this property, set Frequency Span to Span and Center Frequency.

When the number of input samples is not sufficient to achieve the specified resolution bandwidth, the Spectrum Analyzer displays a message similar to this one.

The Spectrum Analyzer removes this message and displays a spectral estimate once you provide enough input samples.