1. DSP for Dummies aka How to turn this (actual raw sonar trace) Into this.. (filtered sonar data)

2. Fundamental property of all analog signals complex signals i.e. audio i.e. digital bitstream Decompose into summation of sinusoids amplitude phase frequency properties

3. Fourier Transform How do we analyze the frequency components of a complex signal Time space x(t) Frequency space X(  ) single frequency signal   t   t  X(  ) is complex -- complex conjugate encodes phase Fourier transform is invertable Some properties

4. Digital Signals Sample amplitude at discrete time intervals.55.46 1,0 -,6 Nyquist limit ( http://www.medcyclopaedia.com) http://www.medcyclopaedia.com (Harry Nyquist, 18891976, Swedish - American physicist), the maximum frequency of a signal that can be measured with a method that employs sampling of the signal with a specific frequency, the sampling frequency. According to Shannons sampling theorem, a signal must be sampled with a frequency at least twice the frequency of the signal itself. The maximum measurable frequency the Nyquist limit or frequency is thus half the sampling frequency. If the signal frequency is higher than the Nyquist limit, aliasing occurs.

5. Discrete Fourier Transform Given a signal represented as a time sequence of samples, the DFT gives us a seqence of frequency/phase amplitudes.55.46 1,0 -,6   

6. Signals and noise What is noise? Any signal other than the one you are interested in! Sources of Noise (the usual suspects) statistical signals from active electronic components crosstalk from other channels or other signals in the same channel signals sensed from external sources (power supply, EM radiation) Trival Example Signal of interest +Noise signal =Noisey Signal Signal to Noise ratio The relative amplitude of the signal of interest o the noise signal

7. Filtering out the Noise Finite Impulse response (FIR) filter Ideal Pulse (time domain) t  Ideal Pulse (frequency domain) to inifinity  Ideal Pulse (time domain) Zero rise/fall time actual rise/fall time finite band of component frequencies The number and values of the component freqencies is related to the rise/fall time of the pulse http://www.chem.uoa.gr/Applets/AppletFourAnal/Appl_FourAnal2.html

8. How a filter works   signal   noise FFT   noise minus FFT -1  signal