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# Multiple Sine Waves in the Time Domain

## Preamble¶

In [14]:

```
# used to create block diagrams
%reload_ext xdiag_magic
%xdiag_output_format svg
import numpy as np # for multi-dimensional containers
import pandas as pd # for DataFrames
import plotly.graph_objects as go # for data visualisation
import plotly.io as pio # to set shahin plot layout
from plotly.subplots import make_subplots
pio.templates['shahin'] = pio.to_templated(go.Figure().update_layout(margin=dict(t=0,r=0,b=40,l=40))).layout.template
pio.templates.default = 'shahin'
```

## Creating Sine Waves¶

In [11]:

```
sample_rate = 1000
start_time = 0
end_time = 10
time = np.arange(start_time, end_time, 1/sample_rate)
frequency = 3
amplitude = 1
theta = 0
sinewave = amplitude * np.sin(2 * np.pi * frequency * time + theta)
fig = go.Figure(layout=dict(xaxis=dict(title='Time (sec)'),yaxis=dict(title='Amplitude')))
fig.add_scatter(x=time, y=sinewave)
fig.show()
```

## Creating Multiple Sine Wave¶

Let's create and plot five sine waves. Let's start by defining our time window and sample rate.

In [52]:

```
sample_rate = 1000
start_time = 0
end_time = 10
theta = 0
time = np.arange(start_time, end_time, 1/sample_rate)
```

`list`

named `frequency`

, and their amplitudes in a `list`

named `amplitude`

.

In [53]:

```
frequency = [3, 5, 2, 1, 10]
amplitude = [1, 2, 7, 3, 0.1]
```

In [54]:

```
fig = make_subplots(rows=5, cols=1, shared_xaxes=True)
for i in range(5):
sinewave = amplitude[i] * np.sin(2 * np.pi * frequency[i] * time + theta)
fig.add_scatter(x=time, y=sinewave, row=i+1, col=1, name=f"wave {i+1}")
fig.show()
```