Signals, Systems and Measurements
Signals, Systems and Measurements tests LTI system properties, convolution, Fourier, Laplace and Z transforms, sampling, and instrument behavior. Measurement questions often hinge on loading and bridge balance.
Core rules
- An LTI system is stable if all poles are in the left half of the s-plane; for discrete systems, inside the unit circle.
- Convolution in time corresponds to multiplication in frequency: y(t) = x(t) * h(t).
- Sampling theorem requires f_s > 2 f_max. Aliased frequency for f_s < 2f is |f - k f_s| with the nearest integer k.
- DFT bin spacing is Delta f = f_s/N; leakage arises when the record is not an integer number of cycles.
- Wheatstone bridge balances when R_1/R_2 = R_3/R_4; a PMMC meter reads average, a true-RMS meter reads RMS.
- Voltmeter loading is reduced by high input impedance; ammeter loading by low resistance.
Worked example
A 1 kHz sinusoid is sampled at 800 Hz. The Nyquist criterion is violated. The alias is |1000 - 1×800| = 200 Hz. The reasoning is that the sampled sequence cannot distinguish 1 kHz from 200 Hz; the nearest multiple of the sampling frequency is subtracted.
Traps
Assuming a higher sampling rate removes aliasing without an anti-alias filter; confusing DFT resolution with analog resolution; ignoring meter loading; and treating a bridge as balanced when detector current is merely small.