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Impulse response of digital filter

`[h,t] = impz(b,a)`

[h,t] = impz(sos)

[h,t] = impz(d)

[h,t] = impz(...,n)

[h,t] = impz(...,n,fs)

impz(...)

`[h,t] = impz(b,a)`

returns
the impulse response of the filter with numerator coefficients, `b`

,
and denominator coefficients, `a`

. `impz`

chooses
the number of samples and returns the response in the column vector, `h`

,
and the sample times in the column vector, `t`

. `t = [0:n-1]'`

and `n`

= `length(t)`

is computed
automatically.

`[h,t] = impz(sos)`

returns the impulse response
for the second-order sections matrix, `sos`

. `sos`

is
a *K*-by-6 matrix, where the number of sections, *K*,
must be greater than or equal to 2. If the number of sections is less
than 2, `impz`

considers the input to be a numerator
vector. Each row of `sos`

corresponds to the coefficients
of a second order (biquad) filter. The *i*th row
of the `sos`

matrix corresponds to ```
[bi(1)
bi(2) bi(3) ai(1) ai(2) ai(3)]
```

.

`[h,t] = impz(d)`

returns the impulse response
of a digital filter, `d`

. Use `designfilt`

to generate `d`

based
on frequency-response specifications.

`[h,t] = impz(...,n)`

computes `n`

samples
of the impulse response when `n`

is an integer (`t`

= `[0:n-1]'`

). If `n`

is
a vector of integers, `impz`

computes the impulse
response at those integer locations, starting the response computation
from 0 (and `t`

= `n`

or `t`

= `[0 n]`

). If, instead
of `n`

, you include the empty vector, `[]`

,
for the second argument, the number of samples is computed automatically.

`[h,t] = impz(...,n,fs)`

computes `n`

samples
and produces a vector `t`

of length `n`

so
that the samples are spaced `1/fs`

units apart.

`impz(...)`

with no output arguments
plots the impulse response of the filter.

`impz`

works for both real and complex input
systems.

If the input to `impz`

is single precision,
the impulse response is calculated using single-precision arithmetic.
The output, `h`

, is single precision.

`impz`

filters a length `n`

impulse
sequence using

filter(b,a,[1 zeros(1,n-1)])

and plots the results using `stem`

.

To compute `n`

in the auto-length case, `impz`

either
uses` n = length(b)`

for
the FIR case or first finds the poles using `p = roots(a)`

, if `length(a)`

is
greater than 1`.`

If the filter is unstable, `n`

is chosen to
be the point at which the term from the largest pole reaches 10^{6} times
its original value.

If the filter is stable, `n`

is chosen to be
the point at which the term due to the largest amplitude pole is 5 × 10^{–5} of
its original amplitude.

If the filter is oscillatory (poles on the unit circle only), `impz`

computes
five periods of the slowest oscillation.

If the filter has both oscillatory and damped terms, `n`

is
chosen to equal five periods of the slowest oscillation or the point
at which the term due to the pole of largest nonunit amplitude is
5 × 10^{–5} of
its original amplitude, whichever is greater.

`impz`

also allows for delays in the numerator
polynomial. The number of delays is incorporated into the computation
for the number of samples.

`designfilt`

| `digitalFilter`

| `impulse`

| `stem`

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