Home smooth filtering shifts my original signal?
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smooth filtering shifts my original signal?

user7084
1#
user7084 Published in May 27, 2018, 3:35 am

Here is my code:

sigma = 10;
sz = 20;
x = linspace(-sz / 2, sz / 2-1, sz);
    gf = exp(-x .^ 2 / (2 * sigma ^ 2));
    gf = gf / sum (gf); % normalize

    f_filter = cconv(gf,f,length(f));

Basically I am Gaussian filtering original signal f. However, when I look at the filtered signal f_filter, there is a shift comparing the original signal f (See attached figure). I am not sure why this is happening. I would like to only smooth but not shift the orginal signal. Please help. Thanks.

my original signal f is here:

-0.0311
-0.0462
-0.0498
-0.0640
-0.0511
-0.0522
-0.0566
-0.0524
-0.0478
-0.0482
-0.0516
-0.0435
-0.0417
-0.0410
-0.0278
-0.0079
-0.0087
-0.0029
0.0105
0.0042
0.0046
0.0107
0.0119
0.0177
0.0077
0.0138
0.0114
0.0103
0.0089
0.0122
0.0122
0.0118
0.0041
0.0047
0.0062
0.0055
0.0033
0.0096
0.0062
-0.0013
0.0029
0.0112
0.0069
0.0160
0.0127
0.0131
0.0039
0.0116
0.0078
0.0018
0.0023
0.0133
0.0140
0.0135
0.0098
0.0100
0.0133
0.0131
0.0086
0.0114
0.0131
0.0175
0.0137
0.0157
0.0040
0.0136
0.0009
0.0049
0.0157
0.0104
0.0038
0.0039
0.0029
0.0126
0.0044
0.0055
0.0040
0.0091
-0.0023
0.0107
0.0151
0.0115
0.0135
0.0160
0.0071
0.0098
0.0094
0.0072
0.0079
0.0055
0.0155
0.0107
0.0108
0.0085
0.0099
0.0055
0.0078
0.0027
0.0121
0.0077
0.0062
0.0021
-0.0019
-0.0003
-0.0022
0.0059
0.0099
0.0114
0.0069
0.0038
0.0020
-0.0031
0.0024
-0.0025
-0.0004
0.0041
0.0059
0.0018
0.0033
0.0130
0.0131
0.0076
0.0084
0.0029
0.0086
0.0078
0.0054
0.0121
0.0101
0.0132
0.0115
0.0074
0.0070
0.0088
0.0017
-0.0003
-0.0060
0.0078
0.0100
0.0044
0.0017
0.0027
0.0062
0.0029
-0.0035
0.0032
0.0060
-0.0035
0.0081
0.0027
0.0043
0.0013
0.0049
0.0119
0.0273
0.0363
0.0435
0.0432
0.0357
0.0424
0.0318
0.0341
0.0354
0.0325
0.0263
0.0320
0.0312
0.0345
0.0407
0.0378
0.0376
0.0334
0.0381
0.0428
0.0375
0.0431
0.0403
0.0395
0.0308
0.0150
0.0006
0.0054
0.0002
0.0090
0.0075
0.0051
0.0067
0.0062
0.0108
0.0059
0.0095
0.0065
0.0087
0.0056
0.0136
0.0057
0.0079
0.0107
0.0106
0.0041
0.0032
0.0106
0.0091
0.0082
0.0025
0.0124
0.0035
0.0034
0.0097
0.0034
0.0050
0.0119
0.0087
0.0081
0.0118
0.0088
0.0050
0.0050
0.0057
0.0118
0.0122
0.0207
0.0112
0.0125
0.0083
0.0125
0.0140
0.0147
0.0237
0.0206
0.0141
0.0164
0.0189
0.0189
0.0136
0.0183
0.0195
0.0209
0.0154
0.0211
0.0254
0.0163
0.0249
0.0236
0.0262
0.0278
0.0285
0.0275
0.0212
0.0277
0.0211
0.0248
0.0289
0.0240
0.0266
0.0479
0.1744
0.4070
0.6818
0.8811
0.9859
0.9347
0.8441
0.7625
0.6396
0.4724
0.3639
0.3406
0.3406
0.3363
0.3318
0.3251
0.3287
0.3135
0.3122
0.3058
0.3103
0.3012
0.2974
0.2995
0.2941
0.2981
0.2968
0.2958
0.2938
0.2929
0.2926
0.2942
0.2982
0.2898
0.2940
0.2927
0.2950
0.2899
0.2979
0.2915
0.2961
0.2921
0.2931
0.2989
0.2941
0.2977
0.3041
0.3042
0.3086
0.3048
0.3069
0.3055
0.3123
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0.3128
0.3115
0.3092
0.3174
0.3152
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0.3080
0.3166
0.3109
0.3103
0.3135
0.3101
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0.3147
0.3044
0.2980
0.2972
0.3013
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0.3069
0.3932
0.6593
0.8921
1.1071
1.2763
1.3947
1.5076
1.6278
1.7452
1.7993
1.8287
1.8470
1.8957
1.9408
1.9791
2.0272
2.0686
2.0974
2.1335
2.1790
2.2134
2.2545
2.2903
2.3163
2.3585
2.3739
2.4126
2.4503
2.4787
2.5198
2.5447
2.5950
2.6228
2.6410
2.6812
2.7123
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2.8584
3.2480
3.5315
3.6808
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3.7471
3.7283
3.6692
3.6718
3.7756
3.9672
4.0376
3.9092
3.7276
3.6586
3.5948
3.6392
3.5671
3.6003
3.6194
3.6350
3.6624
3.6855
3.6958
3.9105
4.3880
5.1342
5.6176
6.3206
7.0392
7.3767
7.5715
7.6516
7.6469
7.5871
7.4591
7.6004
7.5532
7.3601
7.1487
5.9728
4.8974
4.5850
4.4268
4.3352
4.2887
4.3376
4.3182
4.2909
4.2777
4.2548
4.2677
4.2511
4.2817
4.3847
4.4418
4.4696
4.4932
4.4998
4.5151
4.5096
4.5278
4.5139
4.5020
4.4561
4.4067
4.3841
4.3638
4.3750
4.4366
4.5258
4.6565
4.6485
4.5836
4.5183
4.4583
4.3747
4.3509
4.2938
4.2823
4.2844
4.3135
4.3262
4.3255
4.2568
4.2011
4.1832
4.2278
4.2445
4.2409
4.2784
4.2917
4.3035
4.3015
4.3209
4.3204
4.3356
4.3287
4.3260
4.3483
4.3710
4.3798
4.3802
4.3805
4.5162
4.6906
5.0826
5.6588
6.0137
6.2436
6.5361
7.0790
7.6106
7.6410
7.4120
7.4535
7.2476
7.2596
7.1012
7.0986
6.9395
6.5633
5.8438
4.9434
4.6750
4.4320
4.3063
4.2096
4.0193
3.9698
4.0055
4.0218
4.0426
4.0688
4.0650
3.9793
3.9787
3.9766
3.9981
4.0405
4.0165
4.0290
4.0923
4.0897
4.0615
4.0258
4.0008
4.0274
4.0553
4.0646
4.0442
4.0477
3.9986
4.0354
4.0718
4.0563
4.0189
3.8631
3.8144
3.7736
3.8055
3.9730
4.0299
4.0148
3.8265
3.4675
3.3020
3.2474
3.2338
3.1986
3.1680
3.1289
3.0944
3.0523
3.0094
2.9510
2.9246
2.9057
2.8805
2.8545
2.8245
2.7690
2.7236
2.6833
2.6443
2.5969
2.5415
2.4684
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2.3699
2.3293
2.2513
2.1963
2.1285
2.0700
2.0209
1.9575
1.8658
1.6996
1.5120
1.4020
1.3087
1.2166
1.1441
1.0774
1.0226
0.9809
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0.6915
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0.2552
0.2539
0.2527
0.2578
0.2672
0.2701
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0.2658
0.2688
0.2761
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0.2738
0.2774
0.2801
0.2817
0.2803
0.2830
0.2828
0.2876
0.2952
0.2985
0.3016
0.3092
0.3130
0.3153
0.3182
0.3304
0.3471
0.3416
0.3476
0.3497
0.3453
0.3398
0.3448
0.3563
0.3511
0.3502
0.3481
0.3519
0.3573
0.3544
0.3512
0.3489
0.3499
0.3470
0.3533
0.3409
0.3556
0.3474
0.3435
0.3460
0.3519
0.3447
0.3395
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0.3473
0.3453
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0.3484
0.3526
0.3494
0.3607
0.3694
0.4126
0.4604
0.5004
0.5163
0.5328
0.5432
0.5506
0.5485
0.5605
0.5586
0.5622
0.5727
0.5804
0.5797
0.5666
0.5700
0.5696
0.5722
0.5715
0.5656
0.5572
0.5264
0.5156
0.5473
0.6286
0.7503
0.8715
0.8825
0.7507
0.5421
0.2869
0.1091
0.0423
0.0326
0.0343
0.0256
0.0231
0.0281
0.0298
0.0229
0.0283
0.0279
0.0270
0.0300
0.0245
0.0360
0.0280
0.0270
0.0232
0.0276
0.0270
0.0237
0.0197
0.0193
0.0172
0.0140
0.0093
0.0244
0.0226
0.0192
0.0145
0.0124
0.0167
0.0182
0.0111
0.0147
0.0081
0.0151
0.0130
0.0113
0.0131
0.0067
0.0028
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0.0069
0.0082
0.0075
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0.0033
0.0013
0.0011
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0.0009
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0.0098
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0.0067
0.0038
0.0106
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0.0126
0.0134
0.0090
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0.0101
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0.0010
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0.0089
0.0077
0.0064
0.0046
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0.0132
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0.0122
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0.0093
0.0042
0.0042
0.0138
0.0051
-0.0055
-0.0002
0.0048
0.0063
0.0076
0.0016
-0.0005
0.0086
0.0043
-0.0016
0.0100
0.0097
0.0042
0.0092
0.0051
0.0029
0.0044
0.0033
0.0073
0.0093
0.0077
0.0093
0.0021
0.0026
0.0093
0.0068
0.0039
0.0068
0.0041
0.0053
0.0037
0.0075
0.0016
0.0000
-0.0005
0.0073
0.0076
0.0049
0.0046
0.0087
0.0106
0.0072
0.0085
0.0036
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0.0043
0.0201
0.0076
0.0075
0.0134
0.0050
0.0071
0.0032
0.0055
0.0085
0.0046
0.0023
-0.0020
0.0027
0.0060
0.0066
0.0067
0.0014
0.0166
0.0067
0.0024
0.0072
0.0062
0.0081
0.0035
0.0077
0.0101
0.0045
0.0034
0.0144
0.0078
0.0065
0.0093
0.0181
0.0028
0.0050
0.0034
0.0063
0.0150
0.0035
0.0022
0.0079
0.0034
0.0110
0.0075
0.0058
0.0085
0.0152
0.0089
0.0060
0.0017
0.0041
0.0091
0.0072
-0.0109
0.0036
0.0063
0.0080
0.0037
0.0086
0.0097
0.0088
0.0016
0.0057
0.0059
0.0139
0.0061
0.0009
0.0059
0.0126
0.0117
0.0003
0.0060
0.0075
0.0073
0.0080
0.0154
0.0136
0.0121
0.0179
0.0150
0.0125
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