Signal properties (amplitude, frequency, phase) in Signal Processing - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is amplitude in a signal?

Amplitude is the height or strength of the signal wave. It shows how strong or loud the signal is.

beginner

Define frequency in the context of signals.

Frequency is how many times the signal wave repeats in one second. It is measured in Hertz (Hz).

beginner

What does phase mean in a signal?

Phase tells us the position of the wave at a specific time. It shows where the wave starts compared to a reference point.

beginner

How does changing the amplitude affect a signal?

Changing amplitude makes the signal stronger or weaker, like turning volume up or down on a speaker.

beginner

What happens if you increase the frequency of a signal?

Increasing frequency makes the signal wave repeat faster, like a higher-pitched sound.

What unit is frequency measured in?

A Volts (V)

B Seconds (s)

C Hertz (Hz)

D Meters (m)

Frequency is measured in Hertz (Hz), which counts how many cycles happen per second.

If a signal's amplitude increases, what happens?

A The signal becomes stronger

B The signal frequency changes

C The signal becomes weaker

D The signal phase shifts

Amplitude controls the strength of the signal, so increasing it makes the signal stronger.

What does phase describe in a signal?

A The wave's height

B The wave's starting position

C The wave's frequency

D The wave's speed

Phase tells where the wave starts compared to a reference point.

Which property tells how many times a wave repeats per second?

A Frequency

B Amplitude

C Phase

D Wavelength

Frequency counts the number of wave cycles per second.

What happens if the phase of a signal shifts?

A The wave disappears

B The wave repeats faster

C The wave's height changes

D The wave starts at a different point

Phase shift means the wave starts at a different position in time.

Explain the roles of amplitude, frequency, and phase in a signal.

Think about volume, pitch, and timing of a sound wave.

Describe how changing each property (amplitude, frequency, phase) affects a signal's appearance or behavior.

Imagine adjusting volume, pitch, and starting point of a music note.

Practice

1. Which property of a signal describes how tall or strong the wave is?

easy

A. Frequency

B. Amplitude

C. Phase

D. Wavelength

Solution

1. Step 1: Understand amplitude meaning

   Amplitude measures the height or strength of a wave, showing how strong the signal is.

2. Step 2: Compare with other properties

   Frequency is how often the wave repeats, phase shifts the start, wavelength is distance, not height.

3. Final Answer:

   Amplitude -> Option B

4. Quick Check:

   Amplitude = wave height [OK]

Hint: Amplitude means wave height or strength [OK]

Common Mistakes:

• Confusing amplitude with frequency
• Thinking phase affects height
• Mixing wavelength with amplitude

2. Which of the following is the correct way to represent a sine wave with amplitude 3 and frequency 5 Hz in Python using numpy?
t = np.linspace(0, 1, 500)
y = ?

easy

A. 3 + np.sin(2 * np.pi * 5 * t)

B. np.sin(3 * 2 * np.pi * 5 * t)

C. 3 * np.sin(2 * np.pi * 5 * t)

D. 5 * np.sin(2 * np.pi * 3 * t)

Solution

1. Step 1: Recall sine wave formula

   The sine wave formula is amplitude * sin(2π * frequency * time).

2. Step 2: Match formula to options

   3 * np.sin(2 * np.pi * 5 * t) matches amplitude 3 and frequency 5 correctly as 3 * sin(2π * 5 * t).

3. Final Answer:

   3 * np.sin(2 * np.pi * 5 * t) -> Option C

4. Quick Check:

   Amplitude * sin(2π * frequency * t) [OK]

Hint: Amplitude multiplies sine, frequency inside sine argument [OK]

Common Mistakes:

• Multiplying frequency by amplitude inside sine
• Adding amplitude instead of multiplying
• Swapping amplitude and frequency

3. Given the code:
import numpy as np
t = np.linspace(0, 1, 5)
y = 2 * np.sin(2 * np.pi * 1 * t + np.pi/2)
print(np.round(y, 2))
What is the output?

medium

A. [ 2. 0. -2. 0. 2. ]

B. [ 2. 1.41 0. -1.41 -2. ]

C. [ 0. 1.41 2. 1.41 0. ]

D. [ 1.41 2. 1.41 0. -1.41]

Solution

1. Step 1: Calculate time points

   t = [0, 0.25, 0.5, 0.75, 1]

2. Step 2: Compute y values

   y = 2 * sin(2π * 1 * t + π/2) = 2 * cos(2π * t) due to phase shift π/2.
   Values: 2*cos(0)=2, 2*cos(π/2)=0, 2*cos(π)=-2, 2*cos(3π/2)=0, 2*cos(2π)=2
   np.round(y, 2) prints [ 2. 0. -2. 0. 2. ]

3. Final Answer:

   [ 2. 0. -2. 0. 2. ] -> Option A

4. Quick Check:

   Phase π/2 shifts sine to cosine [OK]

Hint: Phase π/2 shifts sine to cosine wave [OK]

Common Mistakes:

• Ignoring phase shift
• Rounding errors
• Mixing sine and cosine values

4. Identify the error in this code snippet that tries to create a sine wave with amplitude 4 and frequency 2 Hz:
import numpy as np
t = np.linspace(0, 1, 100)
y = 4 * np.sin(2 * np.pi * t) * 2

medium

A. The time vector t should be integers, not floats

B. Amplitude should be added, not multiplied

C. np.linspace should use 0 to 2 instead of 0 to 1

D. The frequency multiplier is in the wrong place; it should be inside the sine argument as 2 * np.pi * 2 * t

Solution

1. Step 1: Analyze sine argument order

   The sine argument is 2π * t (frequency 1 Hz), but *2 is outside sin(), incorrectly scaling the amplitude instead of frequency.

2. Step 2: Correct placement for frequency

   Frequency multiplier must be inside sine: 2 * np.pi * 2 * t.

3. Final Answer:

   The frequency multiplier is in the wrong place; it should be inside the sine argument as 2 * np.pi * 2 * t -> Option D

4. Quick Check:

   Frequency must multiply time inside sine [OK]

Hint: Write frequency right after 2π inside sine [OK]

Common Mistakes:

• Multiplying amplitude incorrectly
• Using wrong time vector type
• Changing linspace range unnecessarily

5. You have a signal defined as y = 5 * np.sin(2 * np.pi * 3 * t + π/4). If you want to double the frequency and halve the amplitude while keeping the phase shift the same, which expression is correct?

hard

A. y = 2.5 * np.sin(2 * np.pi * 6 * t + π/4)

B. y = 10 * np.sin(2 * np.pi * 1.5 * t + π/4)

C. y = 2.5 * np.sin(2 * np.pi * 3 * t + π/2)

D. y = 5 * np.sin(2 * np.pi * 6 * t)

Solution

1. Step 1: Adjust amplitude and frequency

   Original amplitude is 5, halved is 2.5. Original frequency is 3, doubled is 6.

2. Step 2: Keep phase shift same

   Phase shift π/4 remains unchanged in the new expression.

3. Final Answer:

   y = 2.5 * np.sin(2 * np.pi * 6 * t + π/4) -> Option A

4. Quick Check:

   Amplitude halved, frequency doubled, phase same [OK]

Hint: Multiply frequency by 2, amplitude by 0.5, keep phase [OK]

Common Mistakes:

• Changing phase shift incorrectly
• Multiplying amplitude instead of halving
• Swapping frequency and amplitude values