Tutorial 1 – Basic concepts in signal analysis, power, energy and spectrum

Download: signals.pdf

23 Comments on “Tutorial 1 – Basic concepts in signal analysis, power, energy and spectrum

  1. Thanks for the very readable tutorial.

    Small error I noticed: Figure 1.7 (“a 3-level signal”) has four levels.


  2. As per my understanding Ux should not come in equation 1.11 because this equation depicts variance with zero mean.

  3. In page 5, it says “However, there is one requirement a carrier must meet: its frequency must be at least two times the highest frequency in the information signal.”

    Shouldn’t it be Sampling frequency for A/D Conversion and its reconstruction? I think it’s been confused with carrier frequency.

    • Yes, you are quite right. The sampling frequency needs to be twice the highest and not carrier. My mistake.


  4. First sentence at the page 7: “If a voice signal is
    on to a carrier, what is the bandwidth
    of the modulated signal? It is still the

    It is usually not the case unless special methods are applied. E.G the bandwidth of simple AM modulated signal is twice the information bandwidth. Theoretically the FM modulated signal bandwidth is infinite (in practice it can be much wider than the information bandwidth)

  5. At the end of page 7 : “If we add many periodic signals, with different frequencies and phases, the resulting signal is still periodic”.

    It is not always the case: if we add two sinusoidal signals which frequencies are 1KHz and sqrt(2) kHz then the result is not periodic.

    • Artak,

      Yes, you are quite right on both, this and the previous item. Short sighted of me to say that.


  6. A very basic doubt (Please bear w/ me):
    Pg 2: “The process of gathering the amplitudes in specific levels is called quantization”
    Pg 3: “The processing of quantization of the discrete signal is called the A/D conversion”

    1. Then what’s diff between quantization and A/D conversion?
    i.e. discrete signal is available by sampling process. Then represent each sample using specific levels by quantization process. The o/p of this is a digital signal i.e. which step in this whole process should be called quantization vs A/D conversion?

    • I think the “sampling the signal” and then its “quantization” should be A/D conversion. Am I correct?

  7. Hi Charan,Thanks you for such an intuitive explanation.
    I am having hardtime understanding Baseband signal bandwidth. Say I am using raised cosine pulses for transmitting signals, how do you define the Bandwidth of this raised cosine pulse? If you say this has bandwidth “B”, does it mean that for generating a raised cosine pulse,we need complex sinusoids of different frequencies from 0 to B ?

    • You determine the bandwidth based on what data rate you want to transmit. So lets say you want to transmit Rs samples per second, then bandwidth is equal to Rs x (1+rolloffFactor).
      However the lowpass bandwidth is one half this. This is how it is defined. The reason is that bandwidth is always a positive quantity. At lowpass half of it is in the negative territory. So lowpass bandwidth by definition is half of the bandpass bandwidth.

      How the RRC pulses created? They are created by passing a signal through a filter. See this matlab link, which might help.


        • Yes, but a bit less. It is possible to transmit (1+alpha)*BW number of samples per Hz in any bandwidth. The alpha is roll off factor, and can be assumed to be about .20.
          To convert this to bits, one multiplies this by the constellation order. M = 2 for QPSK, 3 for 8PSK etc.

          Charan Langton

  8. On page 2: “a digital signal can take any number of values, usually in powers of two”. Can you give a real world example where a digital signal takes values other than the usual binary values ?

  9. Ms Langton, I am grateful for having the opportunity to amble my way through this large resource of useful information on Signals and systems. It is something that I have often struggled with in my work on occasion, and I am not a natural mathematician. There was just the section on Laplace, Z- and discrete transforms that completely lost me in your Signals.pdf. I wondered if you could re-work it again perhaps from a different perspective, and with more information on those sections to make the knowledge ‘full’?
    I have looked at some enquiries made about typos and oversights in your work, do you provide news of updates to your tutorials on your site? It is not clear whether these things have been corrected, as I do not see replies to enquiries that mention whether you have corrected them or not.

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