DSP - ANSWER Digital Signal Processing
ECE 2026 - ANSWER The biggest weed-out class for electrical and computer
engineers at Georgia Institute of Technology.
Sinusoidal Signals - ANSWER A mathematical curve that describes a smooth
repetitive oscillation. It is named after the function sine, of which it is the graph.
It occurs often in pure and applied mathematics, as well as physics, engineering,
signal processing and many other fields. Its most basic form as a function of
time (t) is:
y(t) = A * sin(2π * ft + α )
Amplitude, Phase, and Frequency - ANSWER Amplitude - the maximum
extent of a vibration or oscillation, measured from the position of equilibrium.
Phase - One is the initial angle of a sinusoidal function at its origin and is
sometimes called phase offset or phase difference. Another usage is the fraction
of the wave cycle that has elapsed relative to the origin.
Frequency - frequency is defined as a number of cycles per unit time. This unit
of time often is called the Period(T). So F = 1/T.
, Complex Exponential Representation (Phasors) - ANSWER In physics and
engineering, a phasor (a portmanteau of phase vector[1][2]), is a complex
number representing a sinusoidal function whose amplitude (A), angular
frequency (ω), and initial phase (θ) are time-invariant. It is related to a more
general concept called analytic representation,[3] which decomposes a sinusoid
into the product of a complex constant and a factor that encapsulates the
frequency and time dependence. The complex constant, which encapsulates
amplitude and phase dependence, is known as phasor, complex amplitude, and
(in older texts) sinor, or even complexor.
So the phasor in a sinusoidal function is the non-time-variant real part.
sinusoid = A*cos(wt+θ) = Re{ Ae^i(wt+θ)} =
Re{ Ae^iθ *e^iwt }
Ae^iθ is the phasor
e^iwt is the time-variant part of the sinusoid
See Wiki:
https://en.wikipedia.org/wiki/Phasor
Multiplication of a Phasor by a Scalar - SOLUTION Multiplication of the
phasor {Ae^iθ} by a complex constant, {Be^iФ}, produces another different
phasor. That means its only effect is to change the amplitude and phase of the
underlying sinusoid.
Re{ (Ae^iθ*Be^iФ) * e^iwt } =
Re{ AB*e^i(θ+Ф) * e^iwt} = ABcos(wt+(θ+Ф))
ECE 2026 - ANSWER The biggest weed-out class for electrical and computer
engineers at Georgia Institute of Technology.
Sinusoidal Signals - ANSWER A mathematical curve that describes a smooth
repetitive oscillation. It is named after the function sine, of which it is the graph.
It occurs often in pure and applied mathematics, as well as physics, engineering,
signal processing and many other fields. Its most basic form as a function of
time (t) is:
y(t) = A * sin(2π * ft + α )
Amplitude, Phase, and Frequency - ANSWER Amplitude - the maximum
extent of a vibration or oscillation, measured from the position of equilibrium.
Phase - One is the initial angle of a sinusoidal function at its origin and is
sometimes called phase offset or phase difference. Another usage is the fraction
of the wave cycle that has elapsed relative to the origin.
Frequency - frequency is defined as a number of cycles per unit time. This unit
of time often is called the Period(T). So F = 1/T.
, Complex Exponential Representation (Phasors) - ANSWER In physics and
engineering, a phasor (a portmanteau of phase vector[1][2]), is a complex
number representing a sinusoidal function whose amplitude (A), angular
frequency (ω), and initial phase (θ) are time-invariant. It is related to a more
general concept called analytic representation,[3] which decomposes a sinusoid
into the product of a complex constant and a factor that encapsulates the
frequency and time dependence. The complex constant, which encapsulates
amplitude and phase dependence, is known as phasor, complex amplitude, and
(in older texts) sinor, or even complexor.
So the phasor in a sinusoidal function is the non-time-variant real part.
sinusoid = A*cos(wt+θ) = Re{ Ae^i(wt+θ)} =
Re{ Ae^iθ *e^iwt }
Ae^iθ is the phasor
e^iwt is the time-variant part of the sinusoid
See Wiki:
https://en.wikipedia.org/wiki/Phasor
Multiplication of a Phasor by a Scalar - SOLUTION Multiplication of the
phasor {Ae^iθ} by a complex constant, {Be^iФ}, produces another different
phasor. That means its only effect is to change the amplitude and phase of the
underlying sinusoid.
Re{ (Ae^iθ*Be^iФ) * e^iwt } =
Re{ AB*e^i(θ+Ф) * e^iwt} = ABcos(wt+(θ+Ф))
