Prev Next interpfft

Matrix Column interpolation Via DFT
Syntax y = interpfft(x, N)
Include: include spt\interpfft.oms
See Also expand , resample

ARGUMENTS: 
   INPUTS:   
      x = MATRIX, any numerical type. Input data to be interpolated.
      N = SCALAR, any numerical type, coerced to INTEGER before local
          processing. Requested output row dimension.
   RETURN: MATRIX, DOUBLE, column-wise interpolated data.

Description

Interpolates an input from it's current length to length N by DFT method.

Each column of an input matrix is interpolated to a new length N. N is coerced to INTEGER before local processing. The requested output length must be at least 2, and, >= the input row dimension or 'novalue' is returned. The input matrix must have a row dimension of at least 2 except for the case of a row vector which is treated as a column vector with a row vector returned. All input is converted to DOUBLE before local processing except for the case where the requested row dimension is identical to the input row dimension for which the original data is returned unprocessed. (The imaginary part of COMPLEX input may be interpolated by the call interpfft(1i0*x,N) or interpfft(im(x),N)). Output type is always DOUBLE.

Both the input matrix 'x' and the return value are specified on a uniform grid in the independent variable (the interpolation is with respect to the independent variable).

If the rowdim of input matrix is ODD, a dft(or FFT if power-of-2) is taken and zeros are appended to the middle of the spectrum to extend the length to the requested length. The ifft(or IFFT) is then taken and the result is scaled by the ratio of the requested rowdim to the input rowdim.

If rdim(x) is EVEN and the requested length is EVEN, then split the input spectrum into elements 1 through (N/2+1), and, (N/2+1) through N. This increases length by 1. Add zeros of length Nout-Nin-1 in between. Inverse transform.

Example

# Make a Squarewave
Nin  = 16;                # Input length
Nout = 50;                # Output length
a    = fill( 1, Nin/4, 1) # High Level = +1
b    = fill(-1, Nin/4, 1) # Low  Level = -1
x    = { a, b, a, b }     # Squarewave
y    = interpfft(x, Nout)   # Interpolate

 Plotting both input and output: