Z-transform definition in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the Z-transform summation formula.

Signal Processing

def z_transform(x, z):
    return sum(x[n] * (z ** (-[1])) for n in range(len(x)))

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

An

Bz

Cx

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using z as the exponent instead of n

Using x as the exponent

Using a constant exponent

The Z-transform sums over n, raising z to the power -n.

2fill in blank

medium

Complete the code to calculate the Z-transform for a given sequence x and complex variable z.

Signal Processing

def z_transform(x, z):
    result = 0
    for n in range(len(x)):
        result += x[n] * ([1] ** (-n))
    return result

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

An

Bz

Cx

Dresult

Attempts:

3 left

💡 Hint

Common Mistakes

Using x or n as the base

Using result as the base

The Z-transform formula uses z raised to the power -n.

3fill in blank

hard

Fix the error in the Z-transform function where the exponent is incorrect.

Signal Processing

def z_transform(x, z):
    return sum(x[n] * (z ** (-[1])) for n in range(len(x)))

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

A1

Bz

Cx

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using z as exponent

Using x as exponent

Using a constant exponent

The exponent must be the index n, not z or other variables.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each n to its Z-transform term.

Signal Processing

z_terms = {n: x[n] * ([1] ** (-[2])) for n in range(len(x))}

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

Az

Bn

Cx

Dlen(x)

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping base and exponent

Using x as base or exponent

Each term is x[n] times z to the power -n.

5fill in blank

hard

Fill all three blanks to compute the Z-transform sum using a dictionary comprehension and sum function.

Signal Processing

z_terms = { [1]: x[[2]] * ([3] ** (-[1])) for [1] in range(len(x)) }
result = sum(z_terms.values())

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

An

Bx

Cz

Dlen(x)

Attempts:

3 left

💡 Hint

Common Mistakes

Using x as index

Using wrong base or exponent

The dictionary keys are n, values are x[n] times z to the -n, then sum all values.