The audio signal is a vector in $R^{1000}.$ You will convert it into the coordinate system given by the DCT basis. In

this coordinate system, each basis element corresponds to a cosine function of a different frequency. Thus, the

coordinate vector with respect to the DCT basis tells you how the signal can be written as a linear combination

of cosine waves of different frequencies. To eliminate noise, you replace all entries with absolute value smaller

than $1$ in the coordinate vector by $0.$ Essentially, you suppress certain frequencies by setting them to $0(a$

process from signal processing called filtering$).$ Finally, you transfer the new coordinate vector back into the

coordinate system given by the standard basis.

The audio recording is given to you as a $1$D$-$numpy array stored in audio$\_$signal.

Compute the coordinate vector audio$\_$signal with respect to the DCT$-$basis of $R^{1000}.$ Store the coordinate

vector as a $1$D$-$numpy array in coordinates.

Create a new vector obtained from coordinates by replacing all entries with absolute value smaller than $1$ by

$0.$ Store this new vector as a $1$D$-$numpy array in coordinates$\_$filtered.

Compute the vector in $R^{1000}$ whose coordinate vector in the DCT basis is coordinates$\_$filtered. Store this

vector as a $1$D$-$numpy array in denoised.

The setup code provides the helper function create$\_$dct$\_$basis$(n)$ that creates an $nn$ matrix whose columns

make up the $n-$dimensional DCT basis.

The setup code gives the following variable:

Your code snippet should define the following variable:

user$\_$code.py

import numpy as np

import matplotif.pyplot as plt

# Write your code to calculate denoised audio signal

coordinates $=$dots.

coordinates$\_$filtered $=$dots.

denoised $=...$

# Uncorment below to plot

Hfig, $ax=$ plt$.$subplots$()$

lip$1$t$.$plot$($audio$\_$signa$1)$

ilplt.plot$($denoised$)$