fshift

Shifts the elements of an array by a (possibly non-integer) given number of elements.

Description

FSHIFT shifts the elements in a vector by a given number of elements, as CIRCSHIFT does. However, a non-integer shift value can be used, in which case the elements are shifted along the perfect (sinc-based) interpolation of the periodisation of the vector. For integer shift values, FSHIFT is equivalent to CIRCSHIFT to machine precision.

The syntax to FSHIFT is slightly different from CIRCSHIFT (FSHIFT expects only vectors for its first argument and a scalar for its second argument). Also, the second arguments produces a shift in the opposite direction of CIRCSHIFT to be consistent with the usual statement of the shift property of the Fourier transform.

FSHIFT works by introducing a linear phase into the vector's DFT. As such, if there is a discontinuity between the first and last elements of the input vector, the output vector may present significant ringing.

• MATLAB release: MATLAB 6.5 (R13)

[Matlab User]

Thanks, this was helpful

[Ahmed Fasih]

I had to remove the following from the function: "if isreal(x); y = real(y); end;". With this gone, the output of the fft() of a complex exponential is exactly equal to an fshift()ed sinc().

[Joshua Carmichael]

Helpful.
Two comments:
(1) Is the frequency domain shift appearing as:

exp(-1i*s*pi*f)';

Suppose to include a factor of 2 to be consistent with Matlab's definition of the fft, so that:

exp(-1i*s*2*pi*f)';

(2) Concatenate the input signal with it's flipped version, to make it even, to avoid forcing it to be real, then extract the latter half of the signal.

[Joshua Carmichael]

Never mind, now that I have more carefully read your file, I see that covered the 2*pi factor in the frequency digitization and you are not forcing the signal to be real.