Signals and Systems

Syllabus

1. Signal and its Types (7 hours)
   1. Introduction to signal and signal processing
   2. Classification of signal based on dimension
   3. Classification of one-dimensional signal (CT and DT) and properties
   4. Fundamental signals: Delta function, unit step, ramp, rectangular pulse, signum function
   5. Relationship between unit step and delta function
   6. Signal classification based on causality
   7. Classification of signals based on periodicity (CT and DT)
   8. Transformation of the independent variable
   9. Energy and power signals
   10. Even and odd signals
   11. System, types of systems: linear and non-linear, causal and non-causal, time-invariant and time-variant
2. Fourier Series (9 hours)
   1. Introduction to Fourier series
   2. Fourier series representation of continuous time periodic signal
   3. Properties of continuous time Fourier series: linearity, time shifting, time scaling, time reversal, convolution, multiplication, frequency shifting, conjugate symmetry, Parseval's relation
   4. Fourier series representation of discrete time periodic signal
   5. Properties of discrete time Fourier series: linearity, time shifting, time scaling, time reversal, convolution, modulation, conjugate symmetry, Parseval's relation
   6. Applications of Fourier series
3. Fourier Transform (9 hours)
   1. Introduction to Fourier transform
   2. Continuous time Fourier transform
   3. Properties of continuous time Fourier transform: linearity, time shifting, frequency shifting, time scaling, time reversal, convolution, multiplication, duality, conjugation, Parseval's relation
   4. Discrete time Fourier transform
   5. Properties of discrete time Fourier transform: linearity, time shifting, frequency shifting, time reversal, convolution, modulation, conjugation, Parseval's relation
   6. Fourier transform for periodic signals
   7. Applications of Fourier transform
4. Linear Time Invariant (LTI) System (7 hours)
   1. Linear time invariant (LTI) system
   2. Convolution integral properties of LTI system
   3. Representation of discrete-time signals in terms of impulses
   4. Convolution sum
   5. Representation of continuous-time signals in terms of impulses
   6. Convolution integral
   7. Practical applications of convolution
5. Sampling (6 hours)
   1. Introduction to sampling
   2. Sampling theorem
   3. Practical consideration of sampling and impulse-train sampling
   4. Signal reconstruction from sampled version
   5. Aliasing
   6. Band limited signals
6. Frequency Response of Continuous and Discrete Time Systems (7 hours)
   1. Frequency response of continuous time systems
   2. Transfer function of continuous time system
   3. Impulse response of ideal low-pass, band-pass and high-pass filter
   4. Response of ideal low pass filter to a step function input
   5. Frequency and Impulse response of RC filter
   6. Frequency response of discrete time systems: Transfer function
   7. Impulse response of low-pass, band-pass and high-pass filter

Practicals

1. Generation of continuous and discrete time signals: sinusoidal, unit step, ramp, sinc function, unit impulse, exponential and complex exponential signals
2. Convolution: Square wave with odd symmetry
3. Magnitude and phase of rational signal
4. Fourier series
5. Fourier transform