Transforms
R2026bDSP 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
 | 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 |
 | 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.
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.
Detect Air Compressor Sounds in Simulink Using Wavelet Scattering
Use the Wavelet Scattering block and a pretrained deep learning network to classify audio signals.
Deploy Wavelet Scattering and TensorFlow Lite Network on a Raspberry Pi Using Simulink
Generate and deploy Raspberry Pi® code to detect air compressor sounds using the Wavelet Scattering Simulink block and a pretrained deep learning network.
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.
Teaching Resources
Fourier Analysis
Learn the concepts of frequency, magnitude, and phase, and apply them to Fourier series, and continuous and discrete Fourier transforms.
