Can we band-limit a PCM signal?


Yes -- it's just a matter of selecting the right pulse shape.

(By the way, it makes perfect sense to talk about the bandwidth of a PCM signal; it is, after all, a continuous-time physical signal with bandwidth, energy, power, etc, just like any other signal.)

Most introductory textbooks (irritatingly) assume that a PCM signal must use rectangular pulses. You don't have to, and actually you almost never do, except in the simplest applications.

The PCM signal is a train (or sequence) of pulses with varying amplitudes. This train can be written as $$s_{\text{PCM}}(t) = \sum_k a_k p(t-kT_p),$$ where $T_p$ is the pulse rate, and $a_k$ is the amplitude of each pulse.

In the simplest PCM signal, $a_k$ are either 0 or 1, and $p(t)$ is a rectangular pulse of duration $T_p$. The bandwidth of $s_{\text{PCM}}(t)$ is the same as the bandwidth of $p(t)$, which in this case is (mathematically) infinite.

By selecting a different pulse $p(t)$, you can limit the bandwidth of $s_{\text{PCM}}(t)$. A popular pulse shape is the "raised cosine", which has a bandwidth between $1/T_p$ and $1/2T_p$.

Note that the bandwidth can also be limited by "brute force": just filter the rectangular $s_{\text{PCM}}(t)$ with a low-pass filter of the desired cutoff frequency. This will distort the signal, but in simple applications (high SNR, no further distortion or attenuation) this usually causes no significant performance degradation.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.