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sci.digital-filter-RC-IIR-cutoff Calculator
Calculates the discrete-time IIR filter coefficient α = RC/(RC+Ts) corresponding to an RC low-pass filter at sample rate 1/Ts. Digital RC filter: y[n] = α×y[n−1] + (1−α)×x[n] — this gives the same frequency response as the analogue RC filter, with f_c = (1−α)/(2πα×Ts).
Inputs
Fc Hz
Cycles per second (Hz). Audible sound: 20 Hz – 20 kHz. Make sure units match what the formula expects.
Fs Hz
Amount per unit of time or per unit quantity. Check the denominator before interpreting.
Order N
Reference formula or conversion factor shown for context.
Results
IIR alpha coefficient (Euler method)
The recommended calculation method or analytical approach for these conditions.
alpha (bilinear transform)
The specific form or variant of the result.
rolloff rate (dB/octave)
The value at the specified point or condition.
cutoff-to-Nyquist ratio
The proportional relationship between two quantities.
y[n] = α·x[n] + (1−α)·y[n−1]
Sample size or count used in the calculation.
stability
Measure of how robust the system, structure, or process is to perturbations. Low stability means small changes can cause large deviations.