Sine and Complex Waves

Question 1

What is the distinction between simple and complex waves

Answer 1

Simple Wave: - Sine wave- aka pure tone- (100hz- 440 Hz)
Complex Wave: Defined as a wave that is composed of two or more sine waves
The sine waves that make up complex waves are called components. Waves are combined by superposition( the sum of amplitudes at each moment in time)

Question 2

Describe Complex Periodic waves

Answer 2

Complex Periodic Waves: All complex waves can be described as a sum of simple sine waves
A complex periodic wave is any wave with a regularly repeating pattern that is not a single sine wave.
The frequency components of a complex periodic wave often gave a harmonic relation to the lowest frequency component. (“harmonic”= integer multiple of lowest frequency component)
Frequency components of a complex periodic wave do not have to have a harmonic relation to the lowest frequency component.

Question 3

Describe complex aperiodic waves

Answer 3

Complex Aperiodic Waves: Non repetitive, And by definition there is no fundamental frequency and no harmonics
Examples: Noise- white, blue, brown, pink and in speech: s, ʃ , f , ɵ , t, p, k

Question 4

What are some examples of complex periodic waves

Answer 4

Sawtooth: Odd and even harmonics= Ai = 1/hi dB+ 20log10(1/hi)Slope of spectral envelope is -6dB per octave

Square: Odd harmonics Ai = 1/hi dB+ 20log10(1/hi) Slope of spectral envelope is -6dB per octave Trianguar: Odd Harmonics- Successive amplitudes drop off faster than square waves - Ai=1/hi2dB=20log10(1/h2i)Slope of spectral envelope is -12dB per octave

Single Pulse: A singular rectangular shaped waveform- Aperiodic(pattern does not repeat so no period)Continuous Spectrum for pulse: No line spectrum since aperiodic has all frequencies present Pulse Train: A pulse train is a series of pulses at regular intervals (period T)Line spectrum for a pulse train- only one energy at the even and odd harmonics of the repetition frequency thus, repetition frequency is like a fundamental frequencySpectrum has null points

Question 5

What is the Fourier analysis

Answer 5

Any complex waveform( whether periodic or aperiodic which can be broken down into a sum of different sine waves)

Question 6

What is the waveform synthesis

Answer 6

the process of using superposition to combine several individual sine waves into a single complex waveform

Question 7

Describe the Fourier Series

Answer 7

Any and all complex waves can be represented by the sum of a number of sine waves of differing amplitudes, frequencies and or phases. (A Fourier series is the series of sine waves added together to form a specific complex wave)
The shape of a complex wave is dependent not only on the frequency of the components but also on the magnitude, phase and duration of the components.

Question 8

What does waveform plot

Answer 8

time domain-Displays time as the domain, amplitude as range

Question 9

What does spectrum plot

Answer 9

frequency domain- Displays frequency as the the domain, amplitude as range
types: amplitude, line, continuous, phase

Question 10

What does Waveform display

Answer 10

Waveform displays vibration in time domain and displays waveform amplitude in the range
Cannot determine the frequency components of a complex wave