Just got the TA position for the lecture Digital Audio Signal Processing. It is a class introducing the basic digital audio signal processing. Even so, I thought it better to prepare more for the lecture. So I decided to review the reference book DSP FIRST - A multimedia Approach during the break.

The contents in the book are well-structured and well-explained, and there is nothing tricky inside. All we need to do is to review and use it again and again to make it a solid in our mind. In the blogs, there is nothing else but a list of the key points presented in the book but hopefully, this could help me, and the one who read this, strengthen the understanding.

PS: The contents are based both on the first and the second editions of the book.

  • This is a book about signals and systems.
  • A signal is something that carries information and the system is something that operates the signals.
  • In the other book: A signal is a description of how one parameter varies with another parameter. For instance, the voltage changing over time in an electronic circuit, or brightness varying with distance in an image. A system is any process that produces an output signal in response to an input signal.

1.1 Mathematical representation of signals

  • \(s(t)\): the continuous-time signal
  • \(s[n] = s(nT_s)\): the discrete-time signal, where \(T_s=\frac{1}{f_s}\) is the sampling period with sampling frequency \(f_s\)
  • Same for the image: \(p(x,y) \rightarrow p(m\Delta x, n\Delta y) = p[m, n]\)

1.2 Mathematical representation of systems

  • A system is something that transform signals into new signals or different signal representations: \(y(t) = \mathcal{T}\{x(t)\}\), where the system is represented by the operation \(\mathcal{T}\{\}\).
  • Continuous-time system \(y(t)=\mathcal{T}\{x(t)\}\) and discrete-time system \(y[n]=\mathcal{T}\{x[n]\}\)
  • block diagram: a way of visualization to represent operations and to show the interrelations among the signals.

A block diagram is a diagram of a system in which the principal parts or functions are represented by blocks connected by lines that show the relationships of the blocks. (from wiki)

1.3 Systems as building blocks

Block diagrams are useful for representing complex systems in terms of simpler systems, which are more easily understood.