Equiripple FIR interpolators

`b = fireqint(n,l,alpha)`

b = fireqint(n,l,alpha,w)

b = fireqint('** minorder**',l,alpha,r)

b = fireqint({'

`minorder`

`b = fireqint(n,l,alpha)`

designs
an FIR equiripple filter useful for interpolating input signals. `n`

is
the filter order and it must be an integer. `l`

,
also an integer, is the interpolation factor. `alpha`

is
the bandlimitedness factor, identical to the same feature in `intfilt`

.

`alpha`

is inversely proportional to the transition
bandwidth of the filter. It also affects the bandwidth of the don't-care
regions in the stopband. Specifying `alpha`

allows
you to control how much of the Nyquist interval your input signal
occupies. This can be beneficial for signals to be interpolated because
it allows you to increase the transition bandwidth without affecting
the interpolation, resulting in better stopband attenuation for a
given `l`

. If you set `alpha`

to
1, `fireqint`

assumes that your signal occupies
the entire Nyquist interval. Setting `alpha`

to a
value less than one allows for don't-care regions in the stopband.
For example, if your input occupies half the Nyquist interval, you
could set `alpha`

to 0.5.

The signal to be interpolated is assumed to have zero (or negligible)
power in the frequency band between (`alpha`

*π)
and π. `alpha`

must therefore be a positive
scalar between 0 and 1. `fireqint`

treat such bands
as don't-care regions for assessing filter design.

`b = fireqint(n,l,alpha,w)`

allows
you to specify a vector of weights in `w`

. The number
of weights required in `w`

is given by 1 + `floor`

(`l`

/2). The weights
in `w`

are applied to the passband ripple and stopband
attenuations. Using weights (values between 0 and 1) enables you to
specify different attenuations in different parts of the stopband,
as well as providing the ability to adjust the compromise between
passband ripple and stopband attenuation.

`b = fireqint('`

allows
you to design a minimum-order filter that meets the design specifications. ** minorder**',l,alpha,r)

`r`

is
a vector of maximum deviations or ripples from the ideal filter magnitude
response. When you use the input argument `minorder`

`r`

. The number of elements
required in `r`

is given by 1 + `floor`

(`l/`

2).`b = fireqint({'`

adds
the argument ** minorder**',initord},l,alpha,r)

`initord`

so you can provide an initial
estimate of the filter order. Any positive integer is valid here.
Again, you must provide `r`

, the vector of maximum
deviations or ripples, from the ideal filter magnitude response.Design a minimum order interpolation filter for `l`

=
6 and `alpha`

=
0.8. A vector of ripples must be supplied with
the input argument ** minorder**.

b = fireqint('minorder',6,.8,[0.01 .1 .05 .02]); hm = mfilt.firinterp(6,b); % Create a polyphase interpolator filter zerophase(hm);

Here is the resulting plot of the zerophase response for `hm`

.

For `hm`

, the minimum order filter with the
requested design specifications, here is the filter information.

hm = FilterStructure: 'Direct-Form FIR Polyphase Interpolator' Arithmetic: 'double' Numerator: [1x70 double] InterpolationFactor: 6 PersistentMemory: false

`firgr`

| `firhalfband`

| `firls`

| `firnyquist`

| `intfilt`

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