1. Digital Signal Processing MT5002 Week 1 – Lecture Fundamentals

2. 0. Attendance record

3. Audio Effects Programming Week 1 – Lecture Fundamentals

4. What is a Signal? A signal is defined as a variable parameter that conveys information.

5. What is a Signal? A signal describes the change of a value (amplitude) over time. That value is often the position (or displacement) of a membrane (microphone, loudspeaker, string next to magnetic pickup, etc.)

6. What is a Signal? We will assume that all the signals we deal with will eventually be heard by humans, and therefore will be converted to acoustic energy. Therefore we will obey one of the fundamental laws of physics: energy is neither lost nor gained: it is transformed.

7. Period and Frequency We will define frequency (for sinusoids and waveforms) to be how often a full cycle is repeated in one second. The frequency unit is the Hertz, which means “per second”.

8. Period and Frequency The opposite of frequency is the period; how long it takes for a full cycle to complete. The unit for period is the second (or millisecond.) The relationship is: period = 1 / frequency or: frequency = 1 / period e.g. 100Hz has a period of 0.010sec, or 10ms.

9. Phase Phase refers to the initial starting point of a waveform. By convention a phase of 0 degrees means we start at 0 and go up. The example below would have a phase of about 45 degrees.

10. Phase Phase is by itself inaudible with a single periodic signal. It does however, affect the sum of two signals. The phase difference between two copies of the same signal is often called a phase shift.

11. What is Amplitude? The amplitude of a digital signal is relative to how it is represented. In other words there is no unit for it. The most common convention is to represent signals in a range of [-1,1], with the maximum possible amplitude being one (1).

12. What is Amplitude? This bears no relation to acoustic pressure. That is why we have microphone input level controls and volume knobs. The amplitude of a signal is the largest absolute value in the signal

13. What is the amplitude of this signal? -3,-2,-1,0,1,2,-3,-2,-1,0,1,2,1,0,-1,-2,-4,-3 Min: -4 Max: 2 Amplitude: |-4| = 4

14. What Is Power? The power of a signal is how much energy there is in the signal. To move anything away from a steady state needs energy. The sign of that value only indicates direction.

15. What Is Power? The power of a signal is how much energy there is per unit of time. To calculate it, we add together all the absolute values and divide the sum by the number of values.

16. Example: 0,-1,-2,-3,-2,-1,0,1,2,3,2,1,0,-1,-2,-3,-2,-1,0 Amplitude: 3 Power = (0+1+2+3+2+1+0+...+1+0) / 19 = 27/19 = 1.42

17. Example: 5,5,5,5,5,5,5,5,5,5,5,5,5,5,5 Amplitude: 5 Power = (5+5+5+5+5+...+5) / 15 = 75/15 = 5

18. Comparing Two Signals The amplitude of a signal depends on how we measure it. If we were measuring, for instance, the displacement of a speaker, it might be in a range of +- 3cm; or +- 1in, or +- 30mm. Therefore measuring the values we get when we evaluate peak amplitude or power are arbitrary.

19. Comparing Two Signals To compare two signals, it is more useful to say “signal 1 is twice as powerful as signal 2.” A ratio of 2/1 in the power of two signals roughly corresponds to a perceived doubling of power.

20. Decibels Logarithms are a way to express more simply values that become very large or small. In base 10, log(1000) is 3, because 1000 is 10x10x10. 1 10 2 100 3 1000 4 10000 5 100000 6 1000000 7 10000000

21. Decibels dBm compares to a reference signal of 1 milliwatt. dB(SPL) compares to a signal that is capable of acoustic pressure equivalent to 20 micropascals. There is a 6.02dB amplitude difference between two signals with one double the amplitude of the other.

22. Decibels The decibel (dB) is a unit that allows us to compare two signals. We can compare one signal to a known reference signal, or compare two signals.

23. Arithmetic on Signals Multiplying a signal by a (scalar) value is the same as multiplying every sample in the signal by that value.

24. Arithmetic on Signals Multiplying a signal by 0 makes all the samples 0.

25. Arithmetic on Signals Multiplying a signal by 1 keeps the signal intact. Multiplying a signal by -1 inverts its phase.

26. Arithmetic on Signals Multiplying a signal by 2 increases the amplitude of the signal by 6.02dB Multiplying a signal by 2 increases the power of the signal by 3.01dB

27. Homework 1) What is the difference in dynamic range between 16-bit and 24-bit audio? Why? 2) What is the difference in amplitude (in dB) between a recording played back at 44.1kHz and the same signal played back at 96kHz?

28. Fin.