Signal energy and power in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the energy of a discrete signal x.

Signal Processing

energy = sum(abs(x)[1] 2 )

Drag options to blanks, or click blank then click option'

A**

B-

C+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication operator (*) instead of exponentiation (**).

Adding samples instead of squaring.

The energy of a discrete signal is the sum of the squared magnitudes of its samples. Using ** 2 squares each element.

2fill in blank

medium

Complete the code to calculate the average power of a discrete signal x.

Signal Processing

power = sum(abs(x)[1] 2) / len(x)

Drag options to blanks, or click blank then click option'

A*

B**

C+

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Forgetting to square the samples.

Using multiplication (*) instead of exponentiation (**).

Average power is the sum of squared magnitudes divided by the number of samples. Squaring is done with ** 2.

3fill in blank

hard

Fix the error in the code to compute signal energy correctly.

Signal Processing

energy = sum(x[1] 2 )

Drag options to blanks, or click blank then click option'

A+

B*

C-

D**

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication (*) instead of exponentiation (**).

Not squaring the samples at all.

The energy requires squaring each sample. Using ** 2 correctly squares the values.

4fill in blank

hard

Fill both blanks to create a dictionary of energies for signals longer than 3 samples.

Signal Processing

energies = {name: sum(abs(signal)[1] 2) for name, signal in signals.items() if len(signal) [2] 3}

Drag options to blanks, or click blank then click option'

A**

B>

C<

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication (*) instead of exponentiation (**).

Using wrong comparison operator for filtering.

We square each sample with ** and filter signals longer than 3 using >.

5fill in blank

hard

Fill all three blanks to create a dictionary of average powers for signals with power less than 5.

Signal Processing

powers = {name: sum(abs(signal)[1] 2) / len(signal) for name, signal in signals.items() if sum(abs(signal)[2] 2) / len(signal) [3] 5}

Drag options to blanks, or click blank then click option'

A*

B**

C<

D>

Attempts:

3 left

💡 Hint

Common Mistakes

Using multiplication (*) instead of exponentiation (**).

Using wrong comparison operator for filtering.

Use ** to square samples and < to filter powers less than 5.

Practice

1. What does the energy of a signal represent in signal processing?

easy

A. The frequency content of the signal

B. The average strength of the signal at a single point

C. The total strength of the signal over all time

D. The duration of the signal

Solution

1. Step 1: Understand the definition of signal energy

   Energy is the sum of the squared signal values over time, representing total strength.

2. Step 2: Compare with other options

   Average strength relates to power, frequency content is different, and duration is time length.

3. Final Answer:

   The total strength of the signal over all time -> Option C

4. Quick Check:

   Energy = total signal strength [OK]

Hint: Energy sums signal strength over time, not average [OK]

Common Mistakes:

• Confusing energy with power
• Thinking energy measures frequency
• Assuming energy is signal duration

2. Which of the following formulas correctly calculates the energy \(E\) of a discrete signal \(x[n]\) with \(N\) samples?

easy

A. \(E = \frac{1}{N} \sum_{n=0}^{N-1} |x[n]|\)

B. \(E = \max(|x[n]|)\)

C. \(E = \sum_{n=0}^{N-1} x[n]\)

D. \(E = \sum_{n=0}^{N-1} |x[n]|^2\)

Solution

1. Step 1: Recall energy formula for discrete signals

   Energy is the sum of squared magnitudes of signal samples over all N points.

2. Step 2: Evaluate each option

   \(E = \sum_{n=0}^{N-1} |x[n]|^2\) matches the energy formula. \(E = \frac{1}{N} \sum_{n=0}^{N-1} |x[n]|\) is average magnitude, C is sum without squaring, D is max value.

3. Final Answer:

   \(E = \sum_{n=0}^{N-1} |x[n]|^2\) -> Option D

4. Quick Check:

   Energy = sum of squares [OK]

Hint: Energy sums squared values, not averages or max [OK]

Common Mistakes:

• Using average instead of sum
• Not squaring the signal values
• Taking max instead of sum

3. Consider the discrete signal \(x = [2, -1, 3, 0]\). What is the energy of this signal?

medium

A. 14

B. 6

C. 4

D. 10

Solution

1. Step 1: Square each element of the signal

   Squares: \(2^2=4\), \((-1)^2=1\), \(3^2=9\), \(0^2=0\).

2. Step 2: Sum the squared values

   Sum = 4 + 1 + 9 + 0 = 14.

3. Final Answer:

   14 -> Option A

4. Quick Check:

   Energy = 4+1+9+0 = 14 [OK]

Hint: Square each value, then add all [OK]

Common Mistakes:

• Forgetting to square negative values
• Adding values without squaring
• Miscounting elements

4. The following Python code attempts to calculate the power of a signal \(x = [1, 2, 3, 4]\). What is the error?

import numpy as np
x = [1, 2, 3, 4]
power = np.sum(x**2) / len(x)
print(power)

medium

A. Cannot use ** operator on list directly

B. Division by zero error

C. np.sum is not a function

D. len(x) returns wrong length

Solution

1. Step 1: Identify the data type of x

   x is a Python list, which does not support element-wise power with ** operator.

2. Step 2: Understand numpy operations on lists

   To use ** on elements, x must be a numpy array, not a list.

3. Step 3: Correct code would convert list to array first

   Use x = np.array(x) before power calculation.

4. Final Answer:

   Cannot use ** operator on list directly -> Option A

5. Quick Check:

   List ** 2 causes error [OK]

Hint: Convert list to numpy array before power ops [OK]

Common Mistakes:

• Trying to square list directly
• Ignoring data type errors
• Assuming len(x) causes error

5. A continuous-time signal \(x(t)\) has infinite duration but finite average power. Which statement is true about its energy and power?

hard

A. Energy is finite, power is infinite

B. Energy is infinite, power is finite

C. Both energy and power are infinite

D. Both energy and power are zero

Solution

1. Step 1: Recall definitions for infinite duration signals

   Signals with infinite duration and finite average power have infinite energy because energy sums over all time.

2. Step 2: Understand power for such signals

   Power is average energy per unit time, so it can be finite even if total energy is infinite.

3. Step 3: Match statements with definitions

   Energy is infinite, power is finite correctly states energy infinite and power finite.

4. Final Answer:

   Energy is infinite, power is finite -> Option B

5. Quick Check:

   Infinite duration + finite power = infinite energy [OK]

Hint: Infinite duration signals have infinite energy, finite power [OK]

Common Mistakes:

• Confusing energy and power for infinite signals
• Assuming finite energy for infinite duration
• Mixing definitions of energy and power