I am learning about digital filters and came across the link Why do digital filters work?

In real world communications, I think the input to the channel is in analog after being modulated by digital modulation techniques such as BPSK, Qam etc. These modulation techniques convert the real valued signal to a symbol space. The following questions may seem trivial and can be found in text books, but it is difficult to extract specific information.

  • I am unable to understand, is the input to the channel real valued numbers or symbols?

  • Is the modulated signal passed into the channel? IS the modulated signal digital?

  • If not, Why should we do digital modulation if the signal entering the channel is analog and in which stage do we need digital filters?

An example with a block diagram would be helpful. Thank you


1 Answer 1


I think part of your confusion is actually between discrete-time and digital signals. Some textbooks do not clearly distinguish between them.

All signals that exist in the physical world are real. So, the signals that are produced by any transmitter, and the signal that is picked up by the receiver, are real.

In communications, we say we do "digital communications" when the analog transmitted signal conveys "symbols", which are actually numbers drawn from a finite set. This is different than "analog communications", such as AM and FM radio, where the traansmitted information is a (audio) waveform that can take arbitrary values.

In addition to this, these days communications systems are designed as much as possible using digital signal processing techniques. The nature of these techniques is that they deal with discrete-time (sampled) signals. So, a modern software-defined radio receiver will have an analog antenna, a few analog filters and amplifiers, and an analog quadrature downconverter; then, the analog signal is discretized (sampled) and handed off to a digital signal processor for further processing. The digital signal processing can happen on specialized hardware (such as an FPGA or ASIC), or as software running on a DSP or on a general-purpose CPU. This is where digital filters would be used.

Note that a receiver can be implemented using DSP regardless of whether the underlying communications technology is analog (AM, FM, old TV, etc) or digital (BPSK, QPSK, etc).

  • $\begingroup$ Thank you! You have correctly pointed out my source of confusion. So, just to clarify if my understanding is correct - the signal entering a channel is in symbols and not real valued numbers. $\endgroup$
    – Ria George
    May 13, 2017 at 3:49
  • $\begingroup$ In your question you mentioned "real world" communications, which I understand to mean "physical channels". There are two main types of physical channels: wireline and wireless. The input to a wireline channel is a time-varying voltage. The input to a wireless channel is a radiofrequency propagating wave. Notice that in no case we have "real numbers" going into a physical channel -- that makes no sense. Now, in digital communications the waveform that we put into the channel is a sequence of time-shifted pulses, which encode a sequence of real or complex numbers called "symbols". $\endgroup$
    – MBaz
    May 13, 2017 at 16:21
  • $\begingroup$ For a wireless channel, in the last sentence you say that the waveform entering into the channel is a sequence of time-shifted pulses, which encode a sequence of symbols. So, does this sentence mean that the waveform entering the channel is an encoded waveform and the nature of the encoded waveform is real valued numbers? This part is unclear, can you kindly clarify? $\endgroup$
    – Ria George
    May 13, 2017 at 17:12
  • $\begingroup$ In a wireless channel, using classical modulations such as QPSK, the transmitted waveform is $s(t)=\text{Real}\lbrace e^{j2 \pi f_c t}\sum_{k} a_k p(t-kT_p) \rbrace$, where $f_c$ is the carrier frequency, $R_p=1/T_p$ is the symbol rate, and $p(t-kT_p)$ is a set of orthonormal pulses. The numbers $a_k$ are the symbols transmitted by $s(t)$. They can be complex or real. Note, however, that $s(t)$ is always real. $\endgroup$
    – MBaz
    May 13, 2017 at 19:11
  • $\begingroup$ Is $s(t)$ real part of the symbols, is $s(t)$ symbolic or numeric valued real component? $\endgroup$
    – Ria George
    May 13, 2017 at 20:15

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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