# Documentation

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# Digital Filter Analysis

Magnitude, phase, impulse, and step responses, phase and group delays, pole-zero analysis

Analyze frequency- and time-domain responses of filters. Visualize filter poles and zeros in the complex plane.

## Functions

 `abs` Absolute value (magnitude) `angle` Phase angle `freqz` Frequency response of digital filter `grpdelay` Average filter delay (group delay) `phasedelay` Phase delay of digital filter `phasez` Phase response of digital filter `unwrap` Correct phase angles to produce smoother phase plots `zerophase` Zero-phase response of digital filter `zplane` Zero-pole plot
 `impz` Impulse response of digital filter `impzlength` Impulse response length `stepz` Step response of digital filter
 `filtord` Filter order `filternorm` 2-norm or infinity-norm of digital filter `firtype` Type of linear phase FIR filter `isallpass` Determine whether filter is allpass `isfir` Determine if digital filter has finite impulse response `islinphase` Determine whether filter has linear phase `ismaxphase` Determine whether filter is maximum phase `isminphase` Determine whether filter is minimum phase `isstable` Determine whether filter is stable `fvtool` Open Filter Visualization Tool `sptool` Open interactive digital signal processing tool

## Apps

 Filter Designer Design filters starting with algorithm selection

## Topics

Compensate for the Delay Introduced by an FIR Filter

Use indexing to counteract the time shifts introduced by filtering.

Compensate for the Delay Introduced by an IIR Filter

Remove delays and distortion introduced by filtering, when it is critical to keep phase information intact.

Take Derivatives of a Signal

Use a differentiator filter to differentiate a signal without amplifying the noise.

Speaker Crossover Filters

Devise a simple model of a digital three-way loudspeaker using Chebyshev Type I designs. Visualize the poles, zeros, and frequency responses of the filters.

Frequency Response

Compute and display frequency responses of IIR and FIR lowpass, highpass, and bandpass filters.

Magnitude and Phase

Extract magnitude and phase from a frequency response vector.

Delay

Measure the average time delay of a filter as a function of frequency.

Zero-Pole Analysis

Find and visualize poles and zeros of a linear system.

Impulse Response

Generate and display the impulse response of a simple filter.