Course 1

Signals and Sound

From "what is a signal?" to the door of second-year signal processing: sampling, bits, decibels, converters, filters, harmonics, the spectrum, amplifiers, digital filters, effects and convolution. Each lecture teaches the A Level layer first, then goes deeper for first-year students.

#	Lecture	A Level: the student can	First year: the student can
1	Sound, signals and sampling 25 min	read amplitude, frequency and period from a waveform; apply $f_s > 2f_{\max}$ ; explain aliasing and the anti-alias filter in a PCM system	calculate alias frequencies by folding; show $f$ and $f + f_s$ give the same samples; explain reconstruction and why there is no staircase
2	Bits and resolution coming	apply $\text{resolution} = \text{input range}/2^n$ ; explain quantisation error	derive about 6 dB of signal-to-noise per bit; explain dither and noise shaping
3	Decibels and loudness coming	use ratios and dB for power and voltage; rms and peak values	add sound levels; dB SPL, dBFS, dBu; equal-loudness contours
4	From analogue to digital and back coming	describe flash and ramp ADCs and the op-amp summing DAC; draw the PCM transmitter and receiver	successive-approximation and sigma-delta converters; oversampling
5	Filters I: RC low-pass and high-pass coming	apply $X_C = 1/(2\pi fC)$ and $f = 1/(2\pi RC)$ ; read linear-log and log-log response graphs	the -3 dB point, 20 dB per decade roll-off, phase shift, Bode plots
6	Filters II: active filters and tone controls coming	first-order active filters: bass and treble boost and cut; LC band-pass	second-order filters, Q and resonance; parametric equalisers
7	Harmonics and timbre coming	why instruments playing the same note sound different	Fourier series: square, sawtooth and triangle waves built from sines
8	The spectrum coming	read a spectrum and a spectrogram	the DFT and FFT, frequency resolution, windowing
9	Amplifiers for audio coming	preamplifier, mixer, power amplifier; $P_{\max} = V_s^2/(8R_L)$ ; crossover distortion	negative feedback, distortion measures (THD)
10	Digital filters coming	a moving average smooths a signal	FIR and IIR difference equations; a comb filter
11	Effects coming	what delay, chorus, flanger and reverb do	modulated delay; reverb from comb and all-pass filters; compression
12	Convolution and impulse responses coming	an impulse response as a system's fingerprint	convolution and LTI systems: the bridge to second-year DSP