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# DSP – Digital Signal Processing

Digital signal processing in MatDeck covers a wide variety of signal operations ranging from single to complex. The signals treated in this manner are represented as sequences of samples in time or frequency domains. The potent set of signal operations implemented in MatDeck can be roughly divided into several areas of signal processing. In each area there are plenty of functions and examples that can help users conveniently perform digital signal processing. These several areas and MatDeck functions are:

## Waveform generation

• trigonometric functions – sin(), cos()…
• sinc()
• diric()
• rectangle(), square(), triangle(), sawtooth()

## Signal resampling

• downsample(), upsample(), resample()

## Signal statistics

• average(), median()
• peaks()
• mat min(), columns min(), row min()
• mat max(), columns max(), row max()

## Correlation and convolution

• convolution()
• crosscov()
• crosscorr()

## Digital filter design

### FIR filters

• windowing design: firbandpass(), firbandstop(), firhighpass(), firlowpass()
• frequency sampling: firfreqsampl()
• optimal design: firopt(), firoptord ()

## Digital filter analysis and implementation

• IIR filters: iirfilter(), initiirfilter(), iirfreqresp(), iirgrpdelay(), iirphasedelay()
• FIR filters: firfilter(), initfirfilter(),firfreqresp()

## Signal transforms

• Fast Fourier Transform: fft1(), fft1n(), fft2(), fft2n()
• Inverse Fast Fourier Transform: ffti1(), ffti1n(), ffti2(), ffti2n()
• Discrete Cosine Transform: dct()
• Inverse Discrete Cosine Transform: dcti()
• Inverse Fast Walsh-Hadamard Transform: fwhti()

## Spectral analysis

• Periodogram power spectral density estimate – periodogram()
• Spectrogram using short-time Fourier transform – spectrogram()
• Welch’s power spectral density estimate – powspectwelch()

MatDeck provides several toolkits which enable signal processing operations to be done in a graphical environment, which is extremely beneficial and advantageous for users. The list of signal processing toolkits can be found on the Toolkits page

• Filtering Toolkit – IIR Filtering Form
• Filtering Toolkit for FIR design by windowing and frequency sampling – FIR Filtering Form
• Signal Re-sampling Toolkit – Resampling Form
• Filtering Toolkit for FIR optimal design – FIR Optimal Form
• Waveform Generation Toolkit – Waveform Form
• Correlation and Convolution Toolkit – Correlation Convolution Form
• Signal Transforms Toolkit – Signal Transforms Form
• Signal Statistics Toolkit – Signal Statistics Form