Math & Numerical Methods
Signal Processing Simulators
A focused Math & Numerical Methods hub for signal processing tools, keeping related formulas, assumptions, and engineering checks together.
37 simulators
Adjacent categories
Simulator list
Adaptive Filter Lms Simulator
Signal Processing
Use MSE convergence, estimated filter shape, and stability map to find fast but stable adaptation.
AM/FM Modulation Simulator
Signal Processing
Learn how a message signal such as audio is "carried" by a radio wave through modulation.
Autocorrelation Function Simulator — Period Detection
Signal Processing
Use the biased autocorrelation R_xx[k] to detect the period of a sinusoid buried in noise. Adjust amplitude, frequency, noise and sample count to learn how period estima…
Bit Error Rate (BER) Simulator
Signal Processing
Compute the bit error rate (BER) that decides the quality of a digital link.
Chirp-Z Transform / Zoom-DFT Simulator — High-Resolution Narrow-Band Analysis
Signal Processing
The plain DFT splits 0..F_s/2 into N equal bins. The Chirp-Z transform (CZT) zooms into any range [f_start, f_end] with M bins. Watch two closely spaced tones become res…
Compressive Sensing & L1 Reconstruction Simulator
Signal Processing
A hands-on simulator for compressive sensing: recover a "sparse" N-dimensional signal that has only K non-zero entries from far fewer than Nyquist measurements, using L1…
DFT Leakage Window Detail Simulator
Signal Processing
DFT Leakage Window Detail Simulator updates live numeric results and charts as inputs change, supporting early design checks and model review.
Digital Filter Designer (IIR/FIR)
Signal Processing
Design Butterworth, Chebyshev, and FIR filters. Visualize frequency response, coefficients, and test signals in real-time with this advanced digital filter designer tool.
Dynamic Time Warping (DTW) Simulator
Signal Processing
An interactive tool for Dynamic Time Warping, the classic algorithm that compares two time series whose speed or phase differ by finding the optimal alignment along a st…
Eye Diagram Simulator
Signal Processing
Reproduce the "eye diagram" that shows the quality of a high-speed digital signal at a glance.
FFT Spectrum Analyzer Simulator
Signal Processing
Simulate FFT spectrum analysis with up to 5 sine waves. Explore windowing, spectral leakage, THD, and DFT parameters like frequency resolution in real time.
FIR Filter Design Simulator — Window Method
Signal Processing
Design linear-phase FIR low-pass filters by the window method. Impulse, dB magnitude, transition width, stopband attenuation and group delay update live.
Fourier Epicycles Simulator — Draw Any Curve with Rotating Circles
Signal Processing
Draw any closed curve with your mouse — the DFT decomposes it into spinning circles (epicycles). Adjust the number of circles to see how Fourier approximation quality ch…
Fourier Series Visualizer — Rotating Phasors & Wave Synthesis
Signal Processing
Explore Fourier series synthesis: simulate square, triangle, and sawtooth waves with 1-50 harmonics. Watch Gibbs phenomenon and harmonic spectrum evolve in real-time.
Fourier Series Simulator — Waveform Synthesis & Harmonic Spectrum
Signal Processing
Explore Fourier series synthesis: simulate square, triangle, and sawtooth waves with 1-50 harmonics. Watch Gibbs phenomenon and harmonic spectrum evolve in real-time.
Fourier Transform Visualizer — FFT Spectrum Analyzer
Signal Processing
Explore Fourier transforms interactively. Adjust signals, windows and frequencies with sliders to visualize real-time waveform and spectrum changes.
Goertzel Algorithm Simulator — DTMF Single Frequency Detection
Signal Processing
Detect DTMF tones with the Goertzel algorithm. A second-order IIR filter extracts 8 DFT bins in O(N), ideal for embedded single-tone detection without an FFT.
Hilbert Transform & Analytic Signal — Envelope Detection
Signal Processing
Apply a DFT-based Hilbert transform to an AM signal and extract the instantaneous amplitude, phase and frequency from the analytic signal. Change the carrier frequency a…
Bilinear Transform Simulator — Analog to Digital IIR
Signal Processing
Convert an analog first-order lowpass filter H(s)=ωc/(s+ωc) into a digital IIR filter with the bilinear transform. Change the cutoff and sampling frequency to see the II…
IIR Filter Designer — Butterworth Low-Pass Magnitude Response
Signal Processing
Design a Butterworth low-pass filter and visualize its gain |H(jω)| on a Bode plot. Change cutoff f_c, order N, stopband edge f_s and attenuation A_s to study roll-off.
Laplace Transform Calculator & Visualizer
Signal Processing
Master Laplace transforms with our interactive calculator. Visualize f(t) and F(s), compute partial fractions, and explore pole-zero maps in real time.
Matched Filter Simulator — Pulse Detection in Noise
Signal Processing
Matched filter simulator: detect a known pulse in white noise via convolution. Compute input/output SNR and processing gain in real time, visualize gain = L.
MFCC Feature Simulator — Mel-Frequency Cepstral Coefficients
Signal Processing
Visualize, stage by stage, how a speech signal is turned into MFCC features through pre-emphasis, a Hamming window, FFT, a mel filter bank, logarithm and DCT — the stand…
Mutual Information (MI) Estimation Simulator
Signal Processing
An interactive playground for I(X;Y), the information-theoretic measure of dependence that captures both linear and non-linear relations.
Nyquist Sampling Theorem Simulator — Aliasing of Sampled Signals
Signal Processing
Adjust the signal frequency f, sampling rate f_s, observation duration and bit depth N with sliders, and obtain real-time values of the Nyquist frequency f_s/2, alias fr…
Parseval's Theorem — Energy Conservation in Time and Frequency
Signal Processing
Verify in real time that the time-domain energy of a discrete signal equals its frequency-domain energy under the DFT, using three signal families: sinusoid, rectangular…
Shannon Channel Capacity Simulator — Information Theory Limit
Signal Processing
Compute the Shannon-Hartley capacity C = B·log2(1+S/N) in real time from bandwidth, signal and noise power. Inspect SNR, spectral efficiency and the bandwidth needed to …
Digital Filter Frequency Response Design Tool
Signal Processing
Design and visualize Butterworth, Chebyshev & Bessel IIR filter responses in real time. Adjust type, order, and cutoff frequency instantly.
Signal Modulation Simulator
Signal Processing
Visualize AM, FM, and PM modulation in real time. Adjust parameters like carrier frequency and modulation index to see waveforms and spectra.
Signal & Noise SNR Analyzer
Signal Processing
Analyze signal integrity in real time. Add noise types, compute SNR/ENOB, and visualize results with this interactive CAE tool.
Sampling Theorem & Aliasing Visualizer
Signal Processing
Visualize the Nyquist-Shannon sampling theorem interactively. See real-time aliasing when sampling is too slow and understand the Nyquist frequency.
Spread Spectrum Processing Gain Simulator
Signal Processing
Design a direct-sequence spread spectrum (DSSS) communication link. Adjust the chip rate and data rate to see the processing gain, occupied bandwidth and jamming margin …
Waveform Generator & Synthesizer — RMS, FFT Spectrum, THD Calculator
Signal Processing
Design complex waveforms by combining up to 4 signal components. Instantly analyze key metrics like RMS, THD, and crest factor while visualizing the composite result.
Daubechies-4 Wavelet Simulator — db4 Multiresolution Analysis
Signal Processing
Interactive Daubechies-4 (db4) wavelet simulator: multi-level DWT of 1D signals, thresholding of detail coefficients, and reconstruction MSE. Smoother basis than Haar.
Haar Wavelet Transform Simulator — Multiresolution Analysis and Compression
Signal Processing
Apply the Haar wavelet recursively to a 1D signal and visualize the approximation and detail coefficient pyramid. Learn compression ratio and reconstruction error from t…
Window Function Spectral Comparison — Mainlobe Width and Sidelobe Suppression
Signal Processing
Visualize the spectra of rectangular, Hann, Hamming and Blackman windows. Vary the window length, signal frequency and offset to see the trade-off between spectral leaka…
Z-Transform & Digital Signal System Analyzer
Signal Processing
Visualize and analyze digital filters in real-time. Enter H(z) coefficients to get pole-zero plots, frequency & impulse responses, and stability checks.
How to Use
- Select filter type (Butterworth, Chebyshev, or Bessel) and specify order (2–8)
- Enter cutoff frequency in Hz and sampling rate in kHz to compute normalized digital coefficients
- Input your time-domain signal and run convolution; observe magnitude and phase response in frequency domain
Worked Example
Design a 4th-order Butterworth low-pass filter with cutoff fc=1 kHz and sampling rate fs=10 kHz. Analog prototype has ωc=2π(1000)=6283 rad/s. After bilinear transformation, digital coefficients are b=[0.0201, 0.0804, 0.1206, 0.0804, 0.0201] and a=[1.0, −1.5636, 1.3233, −0.5181, 0.0656]. Filtering a 5 kHz sinusoid (amplitude 1V) yields attenuation of −24 dB at Nyquist normalized frequency 0.5, leaving output peak ≈0.063V.
Practical Notes
- Butterworth maximizes passband flatness; use for audio and general instrumentation where phase distortion is acceptable
- Chebyshev achieves steeper rolloff (6 dB/octave per order) but introduces passband ripple—specify ripple tolerance (0.1–3 dB) before synthesis
- Verify stability via pole-zero plot; all poles must lie inside unit circle for causal IIR filters
- Pre-filter DC offset and high-frequency noise before critical measurements in strain-gauge and accelerometer signals