Signal Processing Calculators

Signal Processing Calculators - Sampling, Aliasing, and Spectral Analysis

Digital signal processing depends on getting the sampling rate right before a single sample is captured. Sample too slowly and high-frequency content folds back into false, lower-frequency data that no downstream processing can fix. The Nyquist Sampling Rate Calculator, Aliasing Frequency Calculator, FFT Bin Resolution and Frequency Calculator, DFT Leakage and Window Function Calculator, and FIR Filter Tap Count and Cutoff Calculator cover the questions every DSP engineer asks before and after sampling a signal, and while designing the filters that clean it up.

Nyquist Sampling Rate Calculator

Nyquist Sampling Rate Calculator - Works in both directions. Enter a signal’s maximum frequency and an oversampling factor to get the minimum Nyquist rate and a practical recommended sampling rate, or enter an existing sampling rate to find the highest frequency (Nyquist frequency) it can capture without aliasing.

Aliasing Frequency Calculator

Aliasing Frequency Calculator - Given a sampling rate and a true input signal frequency, folds the frequency into its apparent, aliased value using the standard folding formula, and reports the Nyquist zone the input falls into.

FFT Bin Resolution and Frequency Calculator

FFT Bin Resolution and Frequency Calculator - Given a sampling rate, FFT size, and bin index, returns the frequency resolution (bin width), the number of usable bins up to the Nyquist limit, the time window the FFT captures, and the exact frequency of any chosen bin.

DFT Leakage and Window Function Calculator

DFT Leakage and Window Function Calculator - Compares Rectangular, Hann, Hamming, and Blackman windows: main lobe width, highest side lobe level, equivalent noise bandwidth, coherent gain, and scalloping loss, scaled to your FFT size and sampling rate.

FIR Filter Tap Count and Cutoff Calculator

FIR Filter Tap Count and Cutoff Calculator - Given a sampling rate, passband edge, stopband edge, and target attenuation, estimates the required FIR tap count using the Kaiser window formula, plus the ideal cutoff frequency and Kaiser beta parameter.

Group Delay Calculator

Group Delay Calculator - Finds a filter’s group delay directly from an FIR filter’s tap count and sampling rate, or from phase measurements at two nearby frequencies using a finite-difference approximation that works for any filter type.

SNR and ENOB Calculator

SNR and ENOB Calculator - Computes an ADC’s ideal quantization SNR from its bit depth, or its real-world effective number of bits (ENOB) and bits lost to noise and distortion from a measured SINAD value.

Quantization Noise and Dynamic Range Calculator

Quantization Noise and Dynamic Range Calculator - Given an ADC’s bit depth and full-scale voltage range, computes the quantization step (LSB), quantization noise RMS voltage, and dynamic range in dB.

Decimation and Interpolation Factor Calculator

Decimation and Interpolation Factor Calculator - Finds the output sampling rate and required anti-alias or anti-imaging filter cutoff when decimating or interpolating a signal by an integer factor.

IIR Filter Pole-Zero Placement Calculator

IIR Filter Pole-Zero Placement Calculator - Places a conjugate pole pair from a target resonant frequency and -3 dB bandwidth, returning pole radius, angle, difference-equation coefficients, stability, and a z-plane diagram.

Butterworth Digital Filter Calculator

Butterworth Digital Filter Calculator - Finds the minimum Butterworth filter order and -3 dB cutoff frequency from passband/stopband edge frequencies and ripple/attenuation specs.

Chebyshev Digital Filter Calculator

Chebyshev Digital Filter Calculator - Finds the minimum Chebyshev Type I filter order and ripple factor for the same passband/stopband spec, and compares it directly against the equivalent Butterworth order.

Convolution Length Calculator

Convolution Length Calculator - Finds the linear convolution output length, the required FFT size, and whether direct or FFT-based convolution needs fewer operations for your signal and filter lengths.

Circular vs Linear Convolution Calculator

Circular vs Linear Convolution Calculator - Checks whether a chosen circular (FFT) convolution length causes time-domain aliasing against the true linear convolution, and reports exactly how many samples are affected.

Z-Transform ROC Calculator

Z-Transform ROC Calculator - Finds the region of convergence for a causal, anticausal, or two-sided sequence from its pole magnitudes, with an automatic BIBO stability check and a z-plane diagram.

Autocorrelation Function Calculator

Autocorrelation Function Calculator - Computes a sinusoid’s autocorrelation at any lag, finds its fundamental period, and plots the periodic Rxx(tau) curve behind classic pitch-detection algorithms.

Cross-Correlation and Time Delay Estimator

Cross-Correlation and Time Delay Estimator - Converts a cross-correlation peak lag into a time delay and distance, for one-way TDOA ranging or round-trip radar and sonar echoes.

Power Spectral Density Calculator

Power Spectral Density Calculator - Computes power spectral density and amplitude spectral density from white noise RMS voltage or a discrete tone captured in an FFT bin.

Short-Time Fourier Transform Resolution Calculator

Short-Time Fourier Transform Resolution Calculator - Finds STFT frequency resolution, time resolution, hop size, and frame rate from window length, sampling rate, and overlap, confirming the uncertainty-principle trade-off.

Wavelet Transform Scale-to-Frequency Calculator

Wavelet Transform Scale-to-Frequency Calculator - Converts a continuous wavelet transform scale into its pseudo-frequency for Morlet, Mexican Hat, or any custom mother wavelet.

Phase Noise and Jitter Calculator

Phase Noise and Jitter Calculator - Converts an oscillator’s phase noise level (dBc/Hz) into RMS phase jitter and RMS time jitter using the standard spot-noise clock jitter formula.

Sigma-Delta Modulator Oversampling Ratio Calculator

Sigma-Delta Modulator Oversampling Ratio Calculator - Finds a sigma-delta ADC’s oversampling ratio, SQNR, and effective number of bits from signal bandwidth, sampling rate, quantizer bit depth, and modulator order.

Matched Filter Output SNR Calculator

Matched Filter Output SNR Calculator - Computes a matched filter’s output SNR from pulse amplitude, duration, and noise power spectral density using the standard 2E/N0 relationship.

Pulse Compression Ratio Calculator

Pulse Compression Ratio Calculator - Finds a radar chirp’s pulse compression ratio, compressed pulse width, and range resolution from uncompressed pulse duration and swept bandwidth.

Cepstrum and Liftering Parameter Calculator

Cepstrum and Liftering Parameter Calculator - Finds a signal’s pitch quefrency and recommended liftering cutoff from sampling rate and fundamental frequency, for speech pitch detection and homomorphic vocoding.

Why Sampling Rate Decisions Matter

The sampling theorem - Formalized by Nyquist and Shannon, the sampling theorem states a signal must be sampled at least twice its highest frequency component (fs ≥ 2 × fmax) to be fully reconstructable. Real systems oversample beyond this minimum because a perfect anti-aliasing filter does not exist in hardware.

Aliasing is irreversible - Once a signal is sampled below its Nyquist rate, frequencies above the Nyquist frequency fold back and corrupt the digitized data permanently. The only defense is an analog anti-aliasing filter placed before the sampler, not digital cleanup afterward.

Frequency vs. time resolution - A larger FFT gives finer frequency resolution (smaller Δf) but requires a longer time window of signal data, trading responsiveness for spectral detail. Choosing FFT size means balancing these two needs for the application at hand.