# Documentation

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# firlp2hp

Convert FIR lowpass filter to Type I FIR highpass filter

## Syntax

```g = firlp2hp(b) g = firlp2hp(b,'narrow') g = firlp2hp(b,'wide') ```

## Description

`g = firlp2hp(b)` transforms the lowpass FIR filter `b` into a Type I highpass FIR filter `g` with zero-phase response Hr(π-w). Filter `b` can be any FIR filter, including a nonlinear-phase filter.

The passband and stopband ripples of `g` will be equal to the passband and stopband ripples of `b`.

`g = firlp2hp(b,'narrow')` transforms the lowpass FIR filter `b` into a Type I narrow band highpass FIR filter `g` with zero-phase response Hr(π-w). `b` can be any FIR filter, including a nonlinear-phase filter.

`g = firlp2hp(b,'wide')` transforms the Type I lowpass FIR filter `b` with zero-phase response Hr(w) into a Type I wide band highpass FIR filter `g` with zero-phase response 1 - Hr(w). Note the restriction that b must be a Type I linear-phase filter.

For this case, the passband and stopband ripples of `g` will be equal to the stopband and passband ripples of `b`.

## Examples

collapse all

Create a narrowband lowpass filter to use as prototype. Display its zero-phase response.

```b = firgr(36,[0 0.2 0.25 1],[1 1 0 0],[1 3]); zerophase(b)```

Convert the prototype filter to a narrowband highpass filter. Add to the plot the zero-phase response of the new filter.

```h = firlp2hp(b); hold on zerophase(h)```

Convert the prototype filter to a wideband highpass filter. Add to the plot the zero-phase response of the new filter.

```g = firlp2hp(b,'wide'); zerophase(g) hold off```

## References

Saramaki, T, Finite Impulse Response Filter Design, Handbook for Digital Signal ProcessingMitra, S.K. and J.F. Kaiser Eds. Wiley-Interscience, N.Y., 1993, Chapter 4.