HIGHPASS

Purpose:

Designs an FIR linear phase highpass filter.

Syntax:

HIGHPASS(order, rate, fc, ripple, attn, fstop)

order	-	Optional. An integer, the filter length. If not specified, the filter order is automatically estimated.
rate	-	A real, the sample rate of the filter in Hertz.
fc	-	A real, the cutoff frequency in Hertz.
ripple	-	Optional. A real, the passband ripple in dB. Defaults to 3 dB.
attn	-	Optional. A real, the stopband attenuation in dB. Defaults to 40 dB.
fstop	-	Optional. A real, the stopband frequency in Hertz. Defaults to fc - 0.05 * rate

Returns:

A series, the highpass filter coefficients. The filter coefficients are identical to the impulse response of the FIR filter.

Example:

W1: highpass(1000.0,100.0)

W1 creates an FIR highpass filter with a sample rate of 1000 Hz and a cutoff frequency of 100 Hz. The stopband frequency defaults to 50 Hz. The resulting filter is 25 samples long with a passband ripple of 1.8 dB and a stopband attenuation of 52 dB.

Example:

W1: highpass(1000.0, 100.0, 3.0, 50.0, 70.0)

W2: 20*log10(filtmag(W1, {1}, 1024))

Creates a similar filter except the desired stopband attenuation is set to 50 dB and the stopband frequency is increased to 70 Hz. The resulting filter contains 45 samples with a passband ripple of 2.27 dB and the stopband attenuation increases to 60 dB. W2 displays the frequency response of the filter.

Example:

W1: highpass(1000.0, 100.0, 3.0, 50.0, 70.0)

W2: gsin(1000, 1/1000, 3) + gsin(1000, 1/1000, 250)

W3: firfilterF(W2, W1)

Creates the same FIR highpass filter as the previous example. W2 contains a series with two sinusoids and W3 applies the filter to recover the higher frequency sinewave.

Remarks:

The HIGHPASS filter specifications are depicted as follows:

HIGHPASS uses the Remez Exchange algorithm to compute the FIR filter coefficients. The Remez Exchange algorithm will attempt to meet or exceed the filter specifications with a linear phase FIR filter.

The filter order refers to the number of resulting filter coefficients, though the order will always be odd for a highpass filter.

The highpass edges must lie between 0.0 and 0.5 * rate (the Nyquist frequency). Overlapping band edges are not permitted.

See KWHPASS to design a linear phase FIR highpass filter with a flat passband using the Kaiser Window method.

See BESSEL, BUTTERWORTH, CHEBY1, CHEBY2 and ELLIPTIC to design IIR filters using the Bilinear Transform method.

HIGHPASS requires the DADiSP/Filters Module.

References:

Oppenheim and Schafer

Digital Signal Processing

Prentice Hall, 1975

Digital Signal Processing Committee

Programs for Digital Signal Processing

I.E.E.E. Press, 1979

HIGHPASS

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