ECE 2026 Digital Signal Processing
Exam Questions and Answers 100%
Solved
DSP - ✔✔Digital Signal Processing
ECE 2026 - ✔✔The biggest weed out class for electrical and computer
engineers at Georgia Institute of Technology.
Sinusoidal Signals - ✔✔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(2\π * ft + α )
Amplitude, Phase, and Frequency - ✔✔Amplitude - the maximum extent of
a vibration or oscillation, measured from the position of equilibrium.
1
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
,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) - ✔✔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 }
2
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
, Ae^iθ is the phasor
e^iwt is the time-variant part of the sinusoid
Refer to Wiki:
https://en.wikipedia.org/wiki/Phasor
Multiplication of a Phasor by a Scalar - ✔✔Multiplication of the phasor
{Ae^iθ} by a complex constant, {Be^iФ}, produces a 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))
Differentiation of a Phasor - ✔✔The time derivative or integral of a phasor
produces a different phasor. That means its only effect is to change the
amplitude and phase of the underlying sinusoid.
Re{ d/dt(Ae^iθ *e^iwt)} =
Re{ Ae^iθ * iwe^iwt },
given i=e^iπ/2, =
Re{ Ae^iθ * e^iπ/2* w * e^iwt } =
3
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
Exam Questions and Answers 100%
Solved
DSP - ✔✔Digital Signal Processing
ECE 2026 - ✔✔The biggest weed out class for electrical and computer
engineers at Georgia Institute of Technology.
Sinusoidal Signals - ✔✔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(2\π * ft + α )
Amplitude, Phase, and Frequency - ✔✔Amplitude - the maximum extent of
a vibration or oscillation, measured from the position of equilibrium.
1
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
,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) - ✔✔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 }
2
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
, Ae^iθ is the phasor
e^iwt is the time-variant part of the sinusoid
Refer to Wiki:
https://en.wikipedia.org/wiki/Phasor
Multiplication of a Phasor by a Scalar - ✔✔Multiplication of the phasor
{Ae^iθ} by a complex constant, {Be^iФ}, produces a 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))
Differentiation of a Phasor - ✔✔The time derivative or integral of a phasor
produces a different phasor. That means its only effect is to change the
amplitude and phase of the underlying sinusoid.
Re{ d/dt(Ae^iθ *e^iwt)} =
Re{ Ae^iθ * iwe^iwt },
given i=e^iπ/2, =
Re{ Ae^iθ * e^iπ/2* w * e^iwt } =
3
©JOSHCLAY 2024/2025. YEAR PUBLISHED 2024.
