Physics 340
Audio Engineering

Review Sheet For Exam #2:

Some of the things you should know for the second exam:

Complex Analysis:

• Understand the simple complex analysis that we did and be able to use it
  Complex exponential
  Euler's theorem: exp(ix) = cos (x) + i sin(x)
• Be able to express the sin(x) and cos(x) as combinations of complex exponentials and vice-versa
  cos(x) = [exp(ix) + exp(-ix)]/2
  sin(x) = [exp(ix) - exp(-ix)]/2i

Fourier Analysis:

• Concept of orthogonal functions
• Understand "Fourier's Trick":
  The integral from -L to L of sin(n pi x/L) * sin(m pi x/L) is zero if n does not equal m
  The integral from -L to L of sin(n pi x/L) * sin(m pi x/L) = L if n = m
  The integral from -L to L of cos(n pi x/L) * cos(m pi x/L) is zero if n does not equal m
  The integral from -L to L of cos(n pi x/L) * cos(m pi x/L) = L if n = m
  The integral from -L to L of cos(n pi x/L) * sin(m pi x/L) is always zero
  
• Know the expressions for the Fourier coefficients on symmetric intervals and be able to use them to find the Fourier coefficients for relatively simple functions.
  More complicated functions will be used than on the previous exam.
  The function I give may or may not be even or odd
  Be able to sketch a function I give
  Be able to take a sketch and figure out the function
• Be able to use an integral table such as Schaum's to do an integral
• Understand the theory of even and odd functions:
  If f(x) = f(-x) then even
  If f(x) = -f(-x) then odd
  Odd x Odd = Even
  Even x Even = Even
  Even x Odd = Odd
  The integral of any odd function over a symmetrical interval (-a to +a) is always zero
  The integral of any even function over a symmetric interval (-a to +a) is twice the integral over one half of the interval (0 to +a)
• Be able to express the fourier coefficients as multiples and/or percentages of the fundamental

Additive Synthesis and SAW:

• Reverse of Fourier analysis
• Allows us to construct any periodic function by adding together a fundamental and its harmonics
• Be thoroughly familiar with SAW and be able to perform any of the activities that we did during class such as:
  Patch in meters into various tracks
  Set meters for post fader operation
  Set meters to indicate levels in percent or dB
  Set level of various tracks to a specified value
  Meter and adjust the output track to prevent overload
  Be able to build a mix to the output track and an output file to observe the waveform
  Load audio files and create regions
  Place regions on various tracks and adjust the phases relative to other waveforms
  Turn the track waveform display off and on
  Zoom and unzoom the waveform display
  Save and load edit list files (EDL files)
  Load in a sound file to look at the waveform

Fourier Transform:

• Extension of Fourier analysis to continuous, rather than discreet, frequencies
• Know the formula for the "forward" continuous Fourier transform H(f)
  Given a simple function for h(t) be able to do the integration and find H(f)
  (Note: don't worry about the limits at infinity. The function h(t) will be such that it is zero outside of some symmetrical interval, so the resulting integral will be from -a to +a)
• Know the formula for the inverse continuous Fourier transform h(t)
  Given a simple function for H(f) be able to do the integration and find h(t)
  (Note: don't worry about the limits at infinity. The function H(f) will be such that it is zero outside of some symmetrical interval, so the resulting integral will be from -a to +a)
• Discreet Fourier transform
  Occurs when h(t) is only known at a set of equally spaced intervals
  Results in a discreet set of coefficients and corresponding frequencies.
  Number of coefficients equals the number of points used for the transform
  Nyquist theorem: highest frequency that can be represented is half of the sampling frequency
  Sampling interval or period = 1/sampling frequency
  

Spectrogram:

• Be able to use Spectrogram to scan files and to do all of the various things we did in class such as:
  Determine the frequency of a soundfile component
  Determine the level of a soundfile component
  Adjust the spectrogram for optimum display of a soundfile
  Turn the coordinate grid on and off
  Save a spectrogram as a .JPG file
  Be able to interpret a spectrogram and correlate the spectrogram with the sound or look at a spectrogram and describe what the sound would be like
• Be able to adjust the spectrogram for optimum display of a soundfile
  Control high and low band frequency limits
  Understand the effect of changing the FFT size on frequency resolution

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If you have any questions or comments, you can send E-Mail to Dr. Greg Latta at glatta@frostburg.edu