In the FFT domain, for example, if I multiply a noise reduction gain to the noisy signal, $ Y(w)H(w) $, this translates to a circular convolution in the time domain of the same length $ y(t) \circledast h(t) $. If I want to convert this to a linear convolution, I should do zero-padding such that the noisy signal y(t) is now twice the original length minus 1 (assuming the noisy signal $ y(t) $ and filtering signal $ h(t) $ are of the same length).
My question is, is obtaining a linear convolution necessary for speech processing? What happens if I just stay with the circular convolution (i.e. NFFT length = signal length)? What if I just want to maintain the same signal length before and after processing? I am quite confused about the importance of satisfying linear convolution property in the context of STFT.