Signals, Systems and Communication Fundamentals
What the exam tests
Signals, Systems and Communication Fundamentals tests LTI system properties, convolution, Fourier/Laplace transforms, sampling, modulation, and noise. Numerical questions often involve bandwidth, bit rate, and SNR.
Core rules
- An LTI system is characterized by its impulse response; output is convolution of input and impulse response.
- Fourier series applies to periodic signals; Fourier transform to energy signals; Laplace transform handles initial conditions and stability.
- Sampling theorem: fs > 2fmax to avoid aliasing; practical systems use anti-aliasing filters and fs above the minimum.
- AM bandwidth = 2fm; FM bandwidth by Carson’s rule ≈ 2(Δf + fm). PCM bit rate = n fs; SNRq ≈ 6.02n + 1.76 dB for full-scale sine.
- Shannon capacity C = B log2(1 + S/N) sets an upper bound, not a modulation guarantee.
Worked example
A 4 kHz audio signal is sampled at the Nyquist rate and encoded with 8 bits per sample. Nyquist rate = 2 × 4 kHz = 8 kHz. Bit rate = 8,000 × 8 = 64 kbps. Quantization SNR ≈ 6.02×8 + 1.76 = 49.9 dB. If the sample rate were reduced to 6 kHz, aliasing would fold 4 kHz components into lower frequencies and the original signal could not be recovered.
Traps
Do not confuse Nyquist rate with Nyquist frequency: rate is 2fmax, frequency is fmax. Do not use the formula SNRq = 6.02n + 1.76 for arbitrary signal distributions without qualification. FM has constant envelope but wider bandwidth. dB gains add; do not multiply them.