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Page 1: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 2: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 3: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 4: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 5: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 6: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 7: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 8: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 9: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 10: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 11: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 12: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 13: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 14: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 15: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 16: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 17: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 18: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 19: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 20: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 21: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 22: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 23: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 24: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 25: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 26: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 27: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 28: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 29: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 30: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 31: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 32: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 33: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 34: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 35: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 36: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 37: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 38: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 39: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 40: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 41: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 42: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 43: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 44: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 45: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 46: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 47: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 48: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 49: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 50: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 51: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 52: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 53: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 54: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 55: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 56: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 57: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 58: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 59: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 60: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 61: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 62: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 63: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 64: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 65: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 66: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 67: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 68: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 69: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 70: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 71: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 72: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 73: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 74: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 75: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 76: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 77: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 78: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 79: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 80: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 81: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 82: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 83: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)
Page 84: Fourier Transforms - 2vda.univie.ac.at/Teaching/SIP/18w/lecturenotes/06_Fourier_Transforms_2.pdf · Fourier Transforms Stretching time compresses frequency. 2 sin w 4 sin '210 X2(jw)