Transforms

Fourier transforms, cosine and wavelet transforms, wavelet scattering

DSP System Toolbox™ offers several System objects and blocks to transform streaming time-domain signals into frequency domain, and vice versa. Techniques such as fast Fourier transform (FFT), short-time Fourier transform, high-resolution FFT, wavelet transforms, and the corresponding inverse operations enable you to analyze the signal in either of the domains and have applications in several fields. For an example, see Analyze a Subband of Input Frequencies Using Zoom FFT. For a MathWorks^® teaching curriculum module on this topic, see Fourier Analysis (MathWorks Teaching Resources).

DSP System Toolbox also offers the Wavelet Scattering block, which creates a framework for wavelet time scattering in the Simulink^® environment. Use this block to derive low-variance features from real-valued data, and then use those features in machine learning and deep learning applications. For more information, see Wavelet Scattering (Wavelet Toolbox). The Wavelet Scattering block requires Wavelet Toolbox™.

Objects

`dsp.FFT`	Discrete Fourier transform
`dsp.IFFT`	Inverse discrete Fourier transform (IDFT)
`dsp.ISTFT`	Inverse short-time FFT
`dsp.STFT`	Short-time FFT
`dsp.ZoomFFT`	High-resolution FFT of a portion of a spectrum

Blocks

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Fourier Transforms

Complex Cepstrum	Compute complex cepstrum of input
FFT	Fast Fourier transform (FFT) of input
IFFT	Inverse fast Fourier transform (IFFT) of input
Inverse Short-Time FFT	Recover time-domain signals by performing inverse short-time fast Fourier transform (FFT)
Magnitude FFT	Compute nonparametric estimate of spectrum using periodogram method
Real Cepstrum	Compute real cepstrum of input
Short-Time FFT	Nonparametric estimate of spectrum using short-time fast Fourier transform (STFT) method
Zoom FFT	High-resolution FFT of a portion of a spectrum

Cosine and Wavelet Transforms

DCT	Discrete cosine transform (DCT) of input
DWT	Compute discrete wavelet transform (DWT) of input or decompose signals into subbands with smaller bandwidths and slower sample rates
IDCT	Inverse discrete cosine transform (IDCT) of input
IDWT	Inverse discrete wavelet transform (IDWT) of input or reconstruct signals from subbands with smaller bandwidths and slower sample rates
Wavelet Scattering	Model wavelet scattering network in Simulink (Since R2022b)

Topics

Transform Time-Domain Data into Frequency Domain
This example shows how to transform time-domain data into the frequency domain using the FFT block.
Transform Frequency-Domain Data into Time Domain
When you want to transform frequency-domain data into the time domain, use the IFFT block.
Linear and Bit-Reversed Output Order
Learn the meaning of linear and bit-reversed data order as used by the FFT and IFFT blocks.
Analyze a Subband of Input Frequencies Using Zoom FFT
Compute the zoom FFT of a sine wave in Simulink.
Speech Enhancement with Gain in Frequency Domain
Denoise a signal by applying selective gain on the signal in the frequency domain. Convert the denoised signal back into time domain and play the signal using Audio Device Writer.
Variable-Size Signal Support DSP System Objects
List of System objects that support variable-sized signals in DSP System Toolbox.

Related Information

Fourier Analysis (MathWorks Teaching Resources)

Featured Examples

Zoom FFT

Showcases zoom FFT, which is a signal processing technique used to analyze a portion of a spectrum at a high resolution. DSP System Toolbox™ offers this functionality in MATLAB® through the dsp.ZoomFFT System object™, and in Simulink® through the Zoom FFT block in the DSP System Toolbox library.

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Detect Air Compressor Sounds in Simulink Using Wavelet Scattering

Use the Wavelet Scattering block and a pretrained deep learning network to classify audio signals.

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Detect Anomalies in ECG Data Using Wavelet Scattering and LSTM Autoencoder in Simulink

Use wavelet scattering and deep learning network to detect anomalies in ECG signals.

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