# Cpsd matlab

The dark mode beta is finally here. Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. And the windows are shifted by Ns data point. The final [Pxy, f] are an average of results obtained from each individual window. Please correct me if I am wrong about this process. My question is, if I use angle Pxy at a specific frequency, say 34Hz.

Does that give me the phase difference between signal x and y at the frequency 34Hz? I am having doubt about this because if Pxy was an average between each individual window, and because each individual was offset by a window shift, doesn't that mean the averaged Pxy 's phase is affected by the window shift? I've tried to correct this by ensuring that the window shift corresponds to an integer of full phase difference corresponding to 34Hz. Is this correct?

I basically have numerous time-series pressure measurement over 60 seconds at Hz sampling rate. Power spectrum analysis indicates that there is a peak frequency at 34 Hz for each signal. FFT analysis of individual window reveals that this peak frequency moves around. So I am not sure if cpsd is the correct way to be going about this. I am currently considering trying to use xcorr to calculate the overall time lag between the signals and then calculate the phase difference from that.

I have also heard of hilbert transform, but I got no idea how that works yet.

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The Overflow Blog. Featured on Meta.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up. I think that the picture is more or less what should be expected.

There is also a strong DC 0 Hz component because the noise has a strong mean, because it ranges from 0 to 1, not -1 to 1. Without the noise the cpsd looks like this. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Asked 5 years, 6 months ago.

Active 5 years, 6 months ago. Viewed 3k times. Active Oldest Votes. Jim Clay Jim Clay But even without knowing that my answer will probably be "no".

The input signals must be of the same size and data type. The Cross-Spectrum Estimator block computes the current power spectrum estimate by averaging the last N power spectrum estimates, where N is the number of spectral averages defined in Number of spectral averages. The block buffers the input data into overlapping segments. You can set the length of the data segment and the amount of data overlap through the parameters set in the block dialog box.

The block computes the power spectrum based on the parameters set in the block dialog box. Each column of the input signal is treated as a separate channel. If the input is a two-dimensional signal, the first dimension represents the channel length or frame size and the second dimension represents the number of channels. If the input is a one-dimensional signal, then it is interpreted as a single channel. Same as input frame length default — Window length is set to the frame size of the input.

Specify on dialog — Window length is the value specified in Window length. Length of the window, in samples, used to compute the spectrum estimate, specified as a positive integer scalar greater than 2. This parameter applies when you set Window length source to Specify on dialog.

The default is This parameter is nontunable. Percentage of overlap between successive data windows, specified as a scalar in the range [ 0, The default is 0. Specify the averaging method as Running or Exponential. In the running averaging method, the block computes an equally weighted average of a specified number of spectrum estimates defined by the Number of spectral averages parameter.

In the exponential method, the block computes the average over samples weighted by an exponentially decaying forgetting factor.

Number of spectral averages, specified as a positive integer scalar. The default is 1. The spectrum estimator computes the current power spectrum estimate by averaging the last N power spectrum estimates, where N is the number of spectral averages defined in Number of spectral averages.

This parameter applies when Averaging method is set to Running. Select this check box to specify the forgetting factor from an input port. When you do not select this check box, the forgetting factor is specified through the Forgetting factor parameter. This parameter applies when Averaging method is set to Exponential.

Specify the exponential weighting forgetting factor as a scalar value greater than zero and smaller than or equal to one. This parameter applies when you set Averaging method to Exponential and clear the Specify forgetting factor from input port parameter.

Auto default — FFT length is set to the frame size of the input. Length of the FFT used to compute the spectrum estimates, specified as a positive integer scalar. This parameter applies when you set FFT length source to Property.Documentation Help Center.

When x is a vector, it is treated as a single channel. When x is a matrix, the PSD is computed independently for each column and stored in the corresponding column of pxx. If x is real-valued, pxx is a one-sided PSD estimate. If x is complex-valued, pxx is a two-sided PSD estimate.

Each segment is windowed with a Hamming window. The modified periodograms are averaged to obtain the PSD estimate. If window is a vector, pwelch divides the signal into segments equal in length to the length of window. The modified periodograms are computed using the signal segments multiplied by the vector, window.

If window is an integer, the signal is divided into segments of length window. The modified periodograms are computed using a Hamming window of length window. The default nfft is the greater of or the next power of 2 greater than the length of the segments.

The sample rate, fsis the number of samples per unit time. For complex-valued signals, f spans the interval [0, fs. To input a sample rate and still use the default values of the preceding optional arguments, specify these arguments as empty, []. The vector w must contain at least two elements, because otherwise the function interprets it as nfft. The vector f must contain at least two elements, because otherwise the function interprets it as nfft.

The frequencies in f are in cycles per unit time. Valid options for freqrange are: 'onesided''twosided'or 'centered'. Reset the random number generator for reproducible results. Plot the Welch PSD estimate. Specify the same FFT length as in the preceding step.

Compute the Welch PSD estimate and verify that it gives the same result as the previous two procedures. The signal has samples. Obtain the Welch PSD estimate dividing the signal into segments samples in length.

The signal segments are multiplied by a Hamming window samples in length. Plot the PSD as a function of normalized frequency.

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The signal is samples in length. The number of overlapped samples is Create a signal consisting of a Hz sinusoid in additive N 0,1 white noise.

The sample rate is 1 kHz and the signal is 5 seconds in duration. Obtain Welch's overlapped segment averaging PSD estimate of the preceding signal. Use a segment length of samples with overlapped samples. Input the sample rate to output a vector of frequencies in Hz. Plot the result. Create a signal consisting of three noisy sinusoids and a chirp, sampled at kHz for 0.

The frequencies of the sinusoids are 1 kHz, 10 kHz, and 20 kHz. The sinusoids have different amplitudes and noise levels. The noiseless chirp has a frequency that starts at 20 kHz and increases linearly to 30 kHz during the sampling.Documentation Help Center.

### Cross Spectrum and Magnitude-Squared Coherence

This example shows how to use the cross spectrum to obtain the phase lag between sinusoidal components in a bivariate time series. The example also uses the magnitude-squared coherence to identify significant frequency-domain correlation at the sine wave frequencies.

But what is the Fourier Transform? A visual introduction.

Create the bivariate time series. The individual series consist of two sine waves with frequencies of and Hz. The series are embedded in additive white Gaussian noise and sampled at 1 kHz. The sine waves in the x -series both have amplitudes equal to 1. The Hz sine wave in the y -series has amplitude 0. You can think of the y -series as the noise-corrupted output of a linear system with input x. Set the random number generator to the default settings for reproducible results. Obtain the magnitude-squared coherence estimate for the bivariate time series.

The magnitude-squared coherence enables you to identify significant frequency-domain correlation between the two time series. Phase estimates in the cross spectrum are only useful where significant frequency-domain correlation exists. To prevent obtaining a magnitude-squared coherence estimate that is identically 1 for all frequencies, you must use an averaged coherence estimator. Set the window length to samples.

This window length contains 10 periods of the Hz sine wave and 20 periods of the Hz sine wave. Use an overlap of 80 samples with the default Hamming window.

Input the sample rate explicitly to get the output frequencies in Hz. Plot the magnitude-squared coherence. The magnitude-squared coherence is greater than 0.

Obtain the cross spectrum of x and y using cpsd. Use the same parameters to obtain the cross spectrum that you used in the coherence estimate. Neglect the cross spectrum when the coherence is small. Plot the phase of the cross spectrum and indicate the frequencies with significant coherence between the two times.

Mark the known phase lags between the sinusoidal components. At Hz and Hz, the phase lags estimated from the cross spectrum are close to the true values. A modified version of this example exists on your system.

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### What is the difference between CSD and CPSD in Signal Processing Toolbox 6.11 (R2009a)?

Search Support Support MathWorks. Search MathWorks. Off-Canvas Navigation Menu Toggle. No, overwrite the modified version Yes. Select a Web Site Choose a web site to get translated content where available and see local events and offers.Documentation Help Center. If x and y are both vectors, they must have the same length. If one of the signals is a matrix and the other is a vector, then the length of the vector must equal the number of rows in the matrix.

The function expands the vector and returns a matrix of column-by-column cross power spectral density estimates. If x and y are matrices with the same number of rows but different numbers of columns, then cpsd returns a three-dimensional array, pxycontaining cross power spectral density estimates for all combinations of input columns.

For real x and ycpsd returns a one-sided CPSD. For complex x or ycpsd returns a two-sided CPSD. This syntax can include any combination of input arguments from previous syntaxes.

To input a sample rate and still use the default values of the preceding optional arguments, specify these arguments as empty, []. Valid options for freqrange are 'onesided''twosided'and 'centered'. Generate two colored noise signals and plot their cross power spectral density. Specify a length FFT and a point triangular window with no overlap. Generate two two-channel sinusoids sampled at 1 kHz for 1 second. The channels of the first signal have frequencies of Hz and Hz.

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The channels of the second signal have frequencies of Hz and Hz. Both signals are embedded in unit-variance white Gaussian noise. Compute the cross power spectral density of the two signals.

Use a sample Bartlett window to divide the signals into segments and window the segments. Specify samples of overlap between adjoining segments and DFT points. Use the built-in functionality of cpsd to plot the result. By default, cpsd works column-by-column on matrix inputs of the same size. Each channel peaks at the frequencies of the original sinusoids. Repeat the calculation, but now append 'mimo' to the list of arguments.Sign in to answer this question. Sign in to comment. Unable to complete the action because of changes made to the page.

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Answers Support MathWorks. Search Support Clear Filters. Support Answers MathWorks. Search MathWorks. MathWorks Answers Support. Open Mobile Search. Trial software. You are now following this question You will see updates in your activity feed. You may receive emails, depending on your notification preferences. MathWorks Support Team on 14 Sep Vote 0. Accepted Answer. Cancel Copy to Clipboard. Depending on the application, this difference may be critical.

This explains the phase inverse observed in the result. CPSD's approach is more natural if one wants to find out the cross power spectral density between x and y.

Use Hanning window instead of Hamming default. Set 'noverlap' to zero. Scale the result with Fs. Pass the input arguments in opposite order.