Using the MATLAB 'symmetric' flag to compute the IFFT of a complex-valued, length-N (with N even), transfer function, the imaginary part of the complex value at the index ((N/2)+1) corresponding to the Nyquist frequency appears to be ignored. Why is this done instead of taking the magnitude of the complex value at the Nyquist frequency? How important are the values at the Nyquist frequency and DC for audio applications?
If you have an exactly conjugate-symmetric frequency domain vector, the values at DC and at Nyquist must be real-valued. The 'symmetric' flag of Matlab's
ifft command makes sure that the result of the inverse FFT is real-valued, implying that the values at DC and Nyquist must also be real-valued.
Let $X[k]$ be the length $N$ DFT of a real-valued sequence $x[n]$:
The value at DC is
which is clearly real-valued if $x[k]$ is real-valued. Similarly, assuming that $N$ is even, the value at Nyquist is
which is also real-valued for real-valued $x[n]$.
Conjugate symmetry means
which for $k=N/2$ (i.e., at Nyquist) gives
Of course, $(5)$ just shows in another way that the bin at Nyquist is real-valued for real-valued $x[k]$.