Signal Processing Formulas
Signal processing formulas connect sampling rate, bandwidth, and frequency resolution in digital systems. These calculators help you avoid aliasing and size FFTs for the resolution you need. They are foundational to DSP and software-defined radio.
Signal Processing Formula Calculators
- FFT Bin Resolution Δf = Fs / N Sampling Frequency 100 Hz, FFT Size (points) 0.025 → Frequency Resolution = 4 kHz
- Averaging SNR Improvement SNR_gain = 10 × log10(N) Number of Averages 0.025 → SNR Improvement = -16.02 dB
- Decimation ENOB Gain ENOB_gain = log2(N) / 2 Oversampling Ratio 0.055 → ENOB Improvement (bits) = -2.092
- FFT Frequency Bin Δf = Fs / N Sample Rate 100 Hz, FFT Points 0.025 → Bin Width = 4 kHz
- Decimation Resolution Gain ENOB_gain = 0.5 × log2(OSR) Oversampling Ratio 0.055 → ENOB Improvement = -2.092
- FFT Processing Gain PG = 10 · log10(M / 2) FFT Length 0.025 → Processing Gain = -19.03 dB
- FFT Noise Floor Floor = SNR + 10·log10(M/2) below FS Converter SNR 0.66 dB, FFT Length 0.025 → Noise Floor Below FS = -18.37 dB
Worked result for every Signal Processing formula
| Formula | Expression | Worked result |
|---|---|---|
| FFT Bin Resolution | Δf = Fs / N | Sampling Frequency 100 Hz, FFT Size (points) 0.025 → Frequency Resolution = 4 kHz |
| Averaging SNR Improvement | SNR_gain = 10 × log10(N) | Number of Averages 0.025 → SNR Improvement = -16.02 dB |
| Decimation ENOB Gain | ENOB_gain = log2(N) / 2 | Oversampling Ratio 0.055 → ENOB Improvement (bits) = -2.092 |
| FFT Frequency Bin | Δf = Fs / N | Sample Rate 100 Hz, FFT Points 0.025 → Bin Width = 4 kHz |
| Decimation Resolution Gain | ENOB_gain = 0.5 × log2(OSR) | Oversampling Ratio 0.055 → ENOB Improvement = -2.092 |
| FFT Processing Gain | PG = 10 · log10(M / 2) | FFT Length 0.025 → Processing Gain = -19.03 dB |
| FFT Noise Floor | Floor = SNR + 10·log10(M/2) below FS | Converter SNR 0.66 dB, FFT Length 0.025 → Noise Floor Below FS = -18.37 dB |
Variables used across Signal Processing formulas
- Δf — Frequency resolution per FFT bin (Hz)
- Fs — Sampling frequency (Hz)
- N — Number of FFT points
- SNR_gain — SNR improvement in decibels (dB)
- ENOB_gain — Additional effective bits of resolution
- OSR — Oversampling ratio
- PG — FFT processing gain (dB)
- M — Number of FFT points
- Floor — FFT noise floor (dB below full scale)
- SNR — Converter signal-to-noise ratio (dB)
Questions people ask about Signal Processing
- What is the bin width of an fft size 52428800 and sample frequency 23.4375mhz — FFT Frequency Bin
Related Formula Categories
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