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|
{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "6b0e891f",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np \n",
"from numpy.fft import fft,ifft,fftshift\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "f7878dca",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([-4, -3, -2, -1, 0, 1, 2, 3])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tau = 1\n",
"freq = np.arange(-4,4)\n",
"freq"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "6b5000a6",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([1.-9.79717439e-16j, 1.-7.34788079e-16j, 1.-4.89858720e-16j,\n",
" 1.-2.44929360e-16j, 1.+0.00000000e+00j, 1.+2.44929360e-16j,\n",
" 1.+4.89858720e-16j, 1.+7.34788079e-16j])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f_tabs = np.exp((-2j*np.pi*freq*tau))\n",
"f_tabs"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "54df500d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(f_tabs.real)\n",
"plt.plot(f_tabs.imag)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bffc82f4",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1.00000000e+00-1.2246468e-16j, -2.95655891e-16+1.2246468e-16j,\n",
" 1.22464680e-16-1.2246468e-16j, -5.07265313e-17+1.2246468e-16j,\n",
" 0.00000000e+00-1.2246468e-16j, 5.07265313e-17+1.2246468e-16j,\n",
" -1.22464680e-16-1.2246468e-16j, 2.95655891e-16+1.2246468e-16j])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"i_tabs = ifft(fftshift(f_tabs))\n",
"i_tabs"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "12ff730b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"shiftet= fftshift(f_tabs)\n",
"plt.plot(shiftet.real)\n",
"plt.plot(shiftet.imag)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "a075dd24",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(i_tabs.real)\n",
"plt.plot(i_tabs.imag)\n",
"plt.show()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "92311556",
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "markdown",
"id": "4c190dbf",
"metadata": {},
"source": [
"# Delay as a Convolution System"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "0929e51c",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[0, 0, 0, 1]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Create the FIR\n",
"D = 3 # Delay value\n",
"h = [0]*D+[1]\n",
"h"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1b8438b2",
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.2"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
|
