How to replace complex numbers in a column vector with 0.000+0.000i ?

Image we obtain a fft of a signal and we wish to remove certain frequencies from the signal. I want to fill in zeros after removing certain rows of complex numbers. Filling in with zeros [0, 0, 0, 0] did not work because ifft was absurd. The real part and the imaginary part must be zeroed and it should appear like 0.0000+0.0000i. Is there a way to fill in 0000+0.0000i in desired regions of the FFT of the signal? What command should one use? Basically this is fft filtering.

Say fft(A) = [-0.0708535039155114 - 0.00736177322883826i, -0.0700055929768761 - 0.0329196686985671i, -0.0593736872430442 + 0.00109491019902367i,

-0.0435002106533236 + 0.0325121703659659i, -0.0605346303385998 - 0.000499071340404484i]

How should we convert that into by removing certain complex numbers and convert them into zero complex numbers?

[-0.0708535039155114 - 0.00736177322883826i, 0.000000 +0.0000000000i, 0.000000 +0.0000000000i, 0.000000 +0.0000000000i,- 0.000499071340404484i]

Thanks.

Answer 1

[Walter Roberson]

Supposing the values are stored in fft_A then

fft_A(2:4) = 0;

is enough. When you display fft_A afterwards you will see the complex zeros are there. The complex 0 component will not show up if you extract the particular value, such as fft_A(2) but it is still stored: you would just be seeing the effect that fft_A(2) would be an expression that calculates a value in some way, and MATLAB automatically checks whether all imaginary components of an expression are 0 and if so drops the complex part.

There are not many circumstances under which you need an array that has all-zero complex part to be explicitly marked as complex. It is possible though:

X = complex(real(X), imag(X));

will have the side effect of marking X as complex even if all the complex components are 0. But as soon as you store anything into X then the complex part would be dropped, and the complex part would be dropped on anything extracted from X.

Answer 2

[Jon]

Suppose you have a complex vector (the result of your fft) lets call it x. If you want to replace some elements of it with zero (0 + 0i), you can just use for example to replace the 3rd and 4th and 6th element with zero

x = randn(10,1) + randn(10,1)*i
x([3 4 6])=0

which gives

0.2939 + 1.3703i

-0.7873 - 1.7115i

0.0000 + 0.0000i

0.0000 + 0.0000i

-1.0689 + 0.3192i

0.0000 + 0.0000i

-2.9443 - 0.8649i

1.4384 - 0.0301i

0.3252 - 0.1649i

-0.7549 + 0.6277i

Note that if the rest of the vector is complex, you can just assign the value 0 (no complex part) to the elements and it will make both the real and imaginary parts zero