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Signals & Systems > Final Exam > Flashcards

Final Exam Flashcards

1
Q

Force (Inertial)

A

Force (inertial) = mass * acceleration

  • newton’s second law of motion
  • measured in Newtons

F=ma

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2
Q

Pressure

A

Pressure = Force/Area

  • measured in Pascals or Newton/m^2
  • 1 pascal = 1 Newton/m^2

P=F/a

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3
Q

Force (Stiffness)

A

Force (stiffness) = -k*displacement - stiffness is measured in kg/sec

  • force of stiffness happening is measured in Newton
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4
Q

Work

A

Wok = force*displacement

  • measured in Joules
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5
Q

Total (forcing force/driving force)

A

Total (or forcing force) = (Mass * acceleration) + (damping or resistance * velocity) + (k*displacement)

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6
Q

For sinusoids ONLY rms is?

A

rms of sinusoid = .707

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7
Q

How does natural frequency relate to mass and stiffness?

A
  • natural frequency is directly proportional to square root of stiffness
  • inversely proportional to square root of mass (directly proportional to 1/square root of mass)
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8
Q

What is the definition of angular velocity?

A

angular velocity = 2f

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9
Q

What is the wavelength in reference to speed and frequency of sound

A

(lambda) = s/f - speed of sound over frequency
- wavelength gets longer as frequency goes down, shorter as it goes up

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10
Q

Mass Reactance

A

Xm= 2(pi)fm

  • frequency
  • mass
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11
Q

Compliant/Stiffness Reactance

A

Xc=1/ [2(pi)fc]

  • frequency
  • compliance
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12
Q

Magnitude of Impedance

A

Z = Sq root [R2 + (Xm-Xc)2]

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13
Q

Law of exponents

A

Xa * Xb = Xa+b

Xa/Xb = Xa-b

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14
Q

Law of Logarithms

A

log (a*b) = log a + log b

log (a/b) = log a - log b

log ab = b log a

log 1/a = -log a

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15
Q

Log10 1

Log10 2

Log10 3

A

Log10 1 = 0.0

Log10 2 = 0.3

Log10 3 = 0.48

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16
Q

Decibels for ratio of intensities

A

dB = 10 log10 (Ix/Ir)

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17
Q

Decibels for ratio of presures

A

dB = 20log10 (Px/Pr)

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18
Q

Reference for intensity level (IL)

A

10-12 watt/m2

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19
Q

Reference for pressure level (SPL)

A

20*10-6 Pa = 20mu pascals

=.00002 Pa

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20
Q

Lps / Lpc

A
  • amount of pressure or energy in 1 Hz band

Lps = SPLwb-10 log10 (change in)fwb

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21
Q

SPLnb

A

SPLnb = SPLwb-10log10 [(change in) fwb / (change in) f]

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22
Q

% of harmonic distortion

A

% harmonic distortion = 100 * [(V22 + V32 +… +Vn2)/V12]

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23
Q

Write a sentence using thefollowing words and phrases: “input signal” “output signal” loudspeaker” “electrical-to-mechanical transducer system” “voltage waveform” and “acoustic waveform”

A
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24
Q

What types of systems perform mechsnical to electrical transformations?

A

The cochlea.

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25
Q

What type of system performs acoustic to mechanical transformations?

A

The middle ear.

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26
Q

Periodic

A

When a signal continualy traces the same path, repeats itself, those that do not are aperiodic

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27
Q

Uniform Circular Motion

A

single point on located in the circumference of a circle traces a sinusoidal function

  • refers to constant speed of the point, rather than velocity because velocity refers to direction as well, however, in this case the point is following around a circle, the direction is set
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28
Q

Length of circumference

A

2πr

r is radius

2πr = 360 degrees

29
Q

Equation for any sinusoid

A

Acos(2πft+ø)

cosine starts at peak (sin instead starts at 0 and goes up)

f = frequency (Hz)

t = time (sec)

Ø = phase angle (degrees)

30
Q

How are clicks and noise similar?

A

HINT: frequency domain

Both have continuous frequency spectra with infinite bandwidth

31
Q

Impulses and white noise, however, have different waveforms. Why do they differ?

A

HINT: Frequency domain

white noise phases are random

impulse spectral components have the same phase D

32
Q

Define “Peak-to-peak” amplitude

A

Measuring amplitude from the distance betwen the highest peak and the lowest valley. Must specify this is the “peak-to-peak” amplitude or else you can’t tell the difference.

33
Q

Peak Amplitude

A

Measuring the amplitude from the high point of the peak to 0.

34
Q

Root Mean Square

A

Square each of the points, add them together and divide that by the number of points. Then you take the square root of that number. This is the average of the wave taking into account the negative numbers. If you just take an average of all of the points you might just wind up with zero. For any sine wave the rms is .707

35
Q

Why is rms amplitude the most important way of specifying the amplitude of a signal?

A

It presupposes the use of a related quantity - intensity. For a sound wave, intensity ina free or completely diffuse fild is proportional to amplitude square.

36
Q

How do you translate from Intensitys to dB?

A

dB = 10 log10 (I/Iref)

37
Q

How do you translate from pressure to dB?

A

dB = 20 log10 (P/Pref)

38
Q

What reference is most important for using SPL?

A

20 micropascals = 20*10-6Pascals = .0002 for use in equation

39
Q

Power

A

power = energy transformed/unit time

measured in joules/sec = watt

joule = Newton * meter (1 joule is a force of 1 newton acting through a distance of 1 meter)

40
Q

Intensity

A

Acoustic Power/ unit area

watts/m2

I=P/a

41
Q

General Property of a logrithm

A

LogB (X) = Y so BY = X

42
Q

What is a system?

A

A system is something which performs some operation on, or transformation of, an input signal to produce an output signal.

43
Q

What do amplifiers do?

A

An amplifier adds energy to a system to increase the power or intensity of a signal.

44
Q

What does an integrator do?

A

?

45
Q

What makes a system linear?

A

A system is linear if the transformation that it performs fulfill the requirements of homogeneity (or propotionality) and additivity.

46
Q

Proportionality (homogeneity)

A

Proportionality: k*inp(t) -> k*outp(t)

47
Q

Additivity

A

if inp1(t) -> outp1(t) and inp2(t) -> outp2(t), inp1(t) + inp2(t) -> outp1(t) + outp2(t)

48
Q

Time invariant

A

A system that does not change over time.

49
Q

When can you predict responses to a system’s input?

A

As long as a system is linear and time invariant (LTI), we only need to know its response to sinusoidal inputs in order to predict its response to any input.

Sinusoidal input signals to an LTI system always lead to a sinusoidal output of the same frequency.

Given that we know the response of an LTI system to sinusoidal stimuli we can predict the system output to any input signal that can be expressed as a sum of sinusoids of the appropriate frequencies and phases (which according to Fourier’s theorem, can be done for nearly any real-world signal).

50
Q

The recipe for predicting outputs of LTI systems:

A

1) determine the transfer function (e.g. the ratios of output-to-input magnitudes and the phase differences, at all necessary frequencies)
2) analyze any arbitrary input into sinusoids (again: amplitudes and phases)
3) synthesize the desired output by a) multiplying the input amplitudes and the system output-to-input magnitudes and b) by summing the input phases with system phases

51
Q

What are the two parts of the transfer function?

A

Amplitude or magnitude response

Phase response

52
Q

Amplitude response

A

Amplitude response = A(f) = output amplitude(f)/input amplitude (f)

53
Q

What is a filter?

A

System that lets some frequencies pass better than others

54
Q

What are the basic types of filters?

A

band-pass

high-pass

low-pass

band-reject/stop

55
Q

How do you find the overall amplitude response of two or more cascaded LTI filters?

A

Cascades of LTI filters combine linearly: to find the overall amplitude response of two or more cascaded LTI filters, all we need to do is multiply the respective amplitude response (gain) curves together (and add the corresponding phases). Note that if the amplitude responses of the LTI filters are expressed in dB, then the dB of the filters are simply added together.

56
Q

What is the “quality factor” of resonant filters?

A

Q - fcf/bandwidth

57
Q

What do we call each resonance of the vocal tract?

A

A Formant

58
Q

What’s so special about a phase response that is a straight-line passing through the origin?

A

A system with a phase response like this has a special property - every sinusoid passed through it is delayed by exactly the same amount of time

59
Q

Amplitude spectrum of sawtooth wave:

A

all harmonics of fundamental, with amplitude of 1/f

60
Q

Amplitude spectrum of a square wave?

A

odd harmonics of fundamental, with amplitude of 1/f

61
Q

amplitude spectrum of triangular wave?

A

odd harmonics of the fundamental, with amplitude of 1/f

62
Q

Amplitude Spectrum of a pulse train

A

DC plus all harmonics of fundamental, with lobed envelope and notches at inverse pulse duration and its multiples

63
Q

From a periodic train of pulses to an impulse (transient, aperiodic signal)

A

indefinitely decrease pulse duration and increase inter-pulse interval

64
Q

6 Steps of the “laborious method”

A

1) analyze the signal into its component sinusoids, specifying the frequency, amplitude, and phase of each of the components (in other words, establish the amplitude and phase spectra of the signal)
2) obtain the amplitude response of the system
3) obtain the phase response of the system
4) for each sinusoid present in the input, use the amplitude response of the system to ascertain the amplitude of each sinusoidal output
5) similarly, taking each sinusoidal input component in turn, establish its output phase from the phase of the input and the phase response of the system
6) now that the amplitude and phases of all the sinusoidal output components are known, the output waveform can be synthesized

65
Q

How do we speed up the “laborious method”

A

By handling the amplitude and phase curves in toto as continous functions and paying attention tot he overall patterns of variation with frequency (e.g. frequency ranges of flat curves, ranges of constant decay or growth)

66
Q

As long as the both the input amplitude spectrum and the amplitude response are expressed in dB…

A

all you need to do is add the two together at corresponding frequencies in order to obtain the amplitude spectrum of the output (again in dB). In a simalr way, the phases of the output componentscan be obtained by adding together the input phases and the phase responses at corresponding frequencies.

67
Q

Wide Bandwidth: Time Resolution, Frequency Resolution & Impulse Response

A

Time Resolution: Good

Frequency Resolution: Bad

Impulse Response: Short

68
Q

Narrow Bandwidth: Time resolution, frequency resolution, impulse response

A

Time: Bad

Frequency: Good

Impulse Response Long

69
Q
A

Signals & Systems (1 decks)

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