Lab

Filter Designer

Design FIR and IIR digital filters, visualize frequency response and pole-zero plots, and export coefficients.

Overview

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JavaScript Required

The Filter Designer requires JavaScript to run in your browser. Please enable JavaScript to use this tool.

Digital filter design

Choose a filter type and design method, adjust parameters, and see the frequency response and pole-zero plot update in real time. Copy coefficients for use in your code.

Filter Configuration

Filter Type

Design Method

Cutoff (normalized): 0.25

Relative to Nyquist (0 to 1)

Order: 31

FIR: 11–127 (odd)

Window

Magnitude & Phase Response

Pole-Zero Plot

Filter Coefficients

b (numerator)

a (denominator)

FIR vs IIR Filters

FIR (Finite Impulse Response)

Always stable. Linear phase possible. Require higher order for sharp transitions. No feedback (a = [1]), only feedforward. This lab includes two FIR methods: windowed sinc (simple, smooth rolloff) and Parks-McClellan (optimal equiripple design via the Remez exchange algorithm).

IIR (Infinite Impulse Response)

Much sharper transitions at low order. Can be unstable if poles move outside the unit circle. Non-linear phase. Designed from analog prototypes via bilinear transform.

Window Functions

Windows taper the ideal filter impulse response to reduce spectral leakage. Hamming and Blackman trade transition width for better sidelobe rejection. Rectangular gives the sharpest transition but worst sidelobes.

Bilinear Transform

Maps the analog s-plane to the digital z-plane via s = 2(z−1)/(z+1). Preserves stability (left half-plane → inside unit circle) but introduces frequency warping, which is corrected by pre-warping the cutoff.

Normalized Cutoff Frequency

Cutoff is expressed as a fraction of the Nyquist frequency (half the sample rate), ranging from 0 to 1. A value of 0.25 means the cutoff is at one-quarter of Nyquist. This normalization makes filter designs independent of the actual sample rate.

Pole-Zero Plot

The z-plane plot shows poles (×) and zeros (ˆ) of the transfer function H(z). Zeros attenuate frequencies, poles amplify them. An IIR filter is stable only if all poles lie inside the unit circle. FIR filters have all poles at the origin, guaranteeing stability.

Filter Order

Order determines the number of coefficients (FIR) or the number of poles and zeros (IIR). Higher order gives a sharper transition band but increases computation, latency, and — for IIR filters — the risk of numerical instability from poles drifting near the unit circle.

Parks-McClellan (Remez Exchange)

An optimal FIR design algorithm that minimizes the maximum weighted approximation error across specified frequency bands. The result is an equiripple filter: the error oscillates uniformly between equal-magnitude peaks. Compared to windowed sinc, Parks-McClellan produces narrower transition bands for the same filter order, at the cost of ripple in the passband and stopband. Use Parks-McClellan when you need precise control over stopband attenuation; use windowed sinc when smooth rolloff matters more.

Security model

Everything runs in your browser. No data is sent to any server. Filter design algorithms (windowed sinc, Remez exchange, bilinear transform, polynomial arithmetic) run entirely in JavaScript on your device.