Filter Project Organization

Day 1:
1. Present Audio Filter Intro PPT
2. Present Sound PPT
   Show speech waveform on cell phone oscilloscope
   Show Fast Fourier Transform of speech waveform on cell phone oscilloscope
3. Present Fourier Series PPT
   Task I: Students do Fourier series for a square wave on graphing calculators
4. Present Filters and Superposition PPT
   Idea of filters introduced
   Key ideas for filtering
     waveform = sum of sinusoids
     filters change sinusoids depending on their frequencies
     use electronic circuit for filter--R, L, C create frequency selective circuits
     can analyze filter for one sinusoid frequency at a time
       i.e., run one frequency (pure tone) through filter at a time and see what happens
     sum filter outputs for all single frequencies to get filter response to waveform
     Summary:
      i)  translate input waveform into Fourier terms (sinusoids or notes or pure tones)
     ii) send each sinusoid through filter
    iii) sum outputs to get response to original waveform
   To build filter, we use electronic circuit.
5. Electronics Intro PPT (basics of electronic components and Kirchhoff's laws)
   Task II: Build first part of circuit that just detects sound input and lights LED

Day 2:
4. Circuits with Sinusoidal Signals PPT
   Filter will be circuit with voltage signal going in (from mp3 player) and signal coming
     out (to speakers)
   We analyze the filter for one frequency of sinusoid at a time
   We use R, L, C to build filter.
   We use K's laws and Ohm's law from Electronics Intro to analyze circuits.
   Plus we use equations for C and L
   R, L, C circuit component equations:  Ohm's law v = iR, Cap i = Cdv/dt, Inductor v = Ldi/dt
   RLC circuits with sinusoidal inputs, all signals in circuit sinusoid of same frequency
   Kirchhoff's laws require that currents and voltages sum to zero--implies sinusoids
     sum to zero.  Could be done with trig identities, but that's hard.
   Worksheet I: Sinusoidal summation using trig
5. Phasors--complex numbers used to sum sinusoids of same frequency
   Map sinusoid to complex number that captures magnitude and phase = phasor
   Think of complex numbers as vectors
   Sum the vectors to figure out sum of sinusoids
   Worksheet II: Sinusoids, finding magnitude, phase, and frequency from waveform
   Worksheet III: Phasors, find phasors and convert rectangular to polar form and back
   Worksheet IV: Sinusoidal summation using phasors (same problem as Worksheet I)
   Phasors capture current versus voltage for circuits using sinusoids with R, L, C.
     v = iR becomes V = IR (I, V = phasors current and voltage, no real change from Ohm's law
     i = Cdv/t becomes I = jwC (I, V = phasors current and voltage, j = sqrt(-1), w = frequency)
     v = Ldi/dt becomes V = jwL (I, V = phasors current and voltage, j = sqrt(-1), w = frequency)
   Circuit problems involve:
     sum of sinusoidal current at nodes
     sum of voltage drops around loop
   Phasors make the sums easier to calculate (as in Worksheet IV versus I)
6. The RLC Filter PPT
   Introduce filter circuit (RLC)
   Give formula for voltage divider that gives filter transfer function
   Discuss mathematics of analyzing transfer function
   Worksheet V: Determine filter center frequency and bandwidth given R, L, and C
   Task III: Design filter for low-pass or high-pass to meet given specs
   Task IV: Build filter and hear its effect on music

Day 3:
   Complete design, construction, and testing of filter circuit