Code the following problem in Python:

The Dow.txt is located below:

12121.71 12136.44 12226.73 12221.93 12194.13 12283.85 12331.6 12309.25 12278.41 12307.48 12328.48 12315.58 12317.5 12416.76 12445.52 12441.27 12471.32 12463.87 12421.25 12343.21 12407.63 12510.57 12501.52 12463.15 12474.52 12480.69 12398.01 12423.49 12416.6 12442.16 12514.98 12556.08 12582.59 12577.15 12567.93 12565.53 12477.16 12533.8 12621.77 12502.56 12487.02 12490.78 12523.31 12621.69 12673.68 12653.49 12661.74 12666.31 12666.87 12637.63 12580.83 12552.55 12654.85 12741.86 12765.01 12767.57 12786.64 12738.41 12686.02 12647.48 12632.26 12216.24 12268.63 12234.34 12114.1 12050.41 12207.59 12192.45 12260.7 12276.32 12318.62 12075.96 12133.4 12159.68 12110.41 12226.17 12288.1 12447.52 12461.14 12481.01 12469.07 12397.29 12300.36 12348.75 12354.35 12382.3 12510.93 12530.05 12560.83 12569.14 12573.85 12484.62 12552.96 12612.13 12720.46 12773.04 12803.84 12808.63 12961.98 12919.4 12953.94 13089.89 13105.5 13120.94 13062.91 13136.14 13211.88 13241.38 13264.62 13312.97 13309.07 13362.87 13215.13 13326.22 13346.78 13383.84 13487.53 13476.72 13556.53 13542.88 13539.95 13525.65 13441.13 13507.28 13521.34 13633.08 13627.64 13668.11 13676.32 13595.46 13465.67 13266.73 13424.39 13424.96 13295.01 13482.35 13553.73 13639.48 13612.98 13635.42 13489.42 13545.84 13360.26 13352.05 13337.66 13427.73 13422.28 13408.62 13535.43 13577.3 13565.84 13611.68 13649.97 13501.7 13577.87 13861.73 13907.25 13950.98 13971.55 13918.22 14000.41 13851.08 13943.42 13716.95 13785.07 13473.57 13265.47 13358.31 13211.99 13362.37 13463.33 13181.91 13468.78 13504.3 13657.86 13270.68 13239.54 13236.53 13028.92 12861.47 12845.78 13079.08 13121.35 13090.86 13236.13 13235.88 13378.87 13322.13 13041.85 13289.29 13238.73 13357.74 13448.86 13305.47 13363.35 13113.38 13127.85 13308.39 13291.65 13424.88 13442.52 13403.42 13739.39 13815.56 13766.7 13820.19 13759.06 13778.65 13878.15 13912.94 13895.63 14087.55 14047.31 13968.05 13974.31 14066.01 14043.73 14164.53 14078.69 14015.12 14093.08 13984.8 13912.94 13892.54 13888.96 13522.02 13566.97 13676.23 13675.25 13671.92 13806.7 13870.26 13792.47 13930.01 13567.87 13595.1 13543.4 13660.94 13300.02 13266.29 13042.74 12987.55 13307.09 13231.01 13110.05 13176.79 12958.44 13010.14 12799.04 12980.88 12743.44 12958.44 13289.45 13311.73 13371.72 13314.57 13248.73 13444.96 13619.89 13625.58 13727.03 13432.77 13473.9 13517.96 13339.85 13167.2 13232.47 13207.27 13245.64 13450.65 13550.04 13551.69 13359.61 13365.87 13264.82 13043.96 13056.72 12800.18 12827.49 12589.07 12735.31 12853.09 12606.3 12778.15 12501.11 12466.16 12159.21 12099.3 11971.19 12270.17 12378.61 12207.17 12383.89 12480.3 12442.83 12650.36 12743.19 12635.16 12265.13 12200.1 12247 12182.13 12240.01 12373.41 12552.24 12376.98 12348.21 12337.22 12427.26 12284.3 12381.02 12570.22 12684.92 12694.28 12582.18 12266.39 12258.9 12213.8 12254.99 12040.39 11893.69 11740.15 12156.81 12110.24 12145.74 11951.09 11972.25 12392.66 12099.66 12361.32 12548.64 12532.6 12422.86 12302.46 12216.4 12262.89 12654.36 12608.92 12626.03 12609.42 12612.43 12576.44 12527.26 12581.98 12325.42 12302.06 12362.47 12619.27 12620.49 12849.36 12825.02 12720.23 12763.22 12848.95 12891.86 12871.75 12831.94 12820.13 13010 13058.2 12969.54 13020.83 12814.35 12866.78 12745.88 12876.05 12832.18 12898.38 12992.66 12986.8 13028.16 12828.68 12601.19 12625.62 12479.63 12548.35 12594.03 12646.22 12638.32 12503.82 12402.85 12390.48 12604.45 12209.81 12280.32 12289.76 12083.77 12141.58 12307.35 12269.08 12160.3 12029.06 12063.09 11842.69 11842.36 11807.43 11811.83 11453.42 11346.51 11350.01 11382.26 11215.51 11288.53 11231.96 11384.21 11147.44 11229.02 11100.54 11055.19 10962.54 11239.28 11446.66 11496.57 11467.34 11602.5 11632.38 11349.28 11370.69 11131.08 11397.56 11583.69 11378.02 11326.32 11284.15 11615.77 11656.07 11431.43 11734.32 11782.35 11642.47 11532.96 11615.93 11659.9 11479.39 11348.55 11417.43 11430.21 11628.06 11386.25 11412.87 11502.51 11715.18 11543.55 11516.92 11532.88 11188.23 11220.96 11510.74 11230.73 11268.92 11433.71 11421.99 10917.51 11059.02 10609.66 11019.69 11388.44 11015.69 10854.17 10825.17 11022.06 11143.13 10365.45 10850.66 10831.07 10482.85 10325.38 9955.5 9447.11 9258.1 8579.19 8451.19 9387.61 9310.99 8577.91 8979.26 8852.22 9265.43 9045.21 8519.21 8691.25 8378.95 8175.77 9065.12 8990.96 9180.69 9325.01 9319.83 9625.28 9139.27 8695.79 8943.81 8870.54 8693.96 8282.66 8835.25 8497.31 8273.58 8424.75 7997.28 7552.29 8046.42 8443.39 8479.47 8726.61 8829.04 8149.09 8419.09 8591.69 8376.24 8635.42 8934.18 8691.33 8761.42 8565.09 8629.68 8564.53 8924.14 8824.34 8604.99 8579.11 8519.69 8419.49 8468.48 8515.55 8483.93 8668.39 8776.39 9034.69 8952.89 9015.1 8769.7 8742.46 8599.18 8473.97 8448.56 8200.14 8212.49 8281.22 7949.09 8228.1 8122.8 8077.56 8116.03 8174.73 8375.45 8149.01 8000.86 7936.83 8078.36 7956.66 8063.07 8280.59 8270.87 7888.88 7939.53 7932.76 7850.41 7552.6 7555.63 7465.95 7365.67 7114.78 7350.94 7270.89 7182.08 7062.93 6763.29 6726.02 6875.84 6594.44 6626.94 6547.05 6926.49 6930.4 7170.06 7223.98 7216.97 7395.7 7486.58 7400.8 7278.38 7775.86 7660.21 7749.81 7924.56 7776.18 7522.02 7608.92 7761.6 7978.08 8017.59 7975.85 7789.56 7837.11 8083.38 8057.81 7920.18 8029.62 8125.43 8131.33 7841.73 7969.56 7886.57 7957.06 8076.29 8025 8016.95 8185.73 8168.12 8212.41 8426.74 8410.65 8512.28 8409.85 8574.65 8418.77 8469.11 8284.89 8331.32 8268.64 8504.08 8474.85 8422.04 8292.13 8277.32 8473.49 8300.02 8403.8 8500.33 8721.44 8740.87 8675.24 8750.24 8763.13 8764.49 8763.06 8739.02 8770.92 8799.26 8612.13 8504.67 8497.18 8555.6 8539.73 8339.01 8322.91 8299.86 8472.4 8438.39 8529.38 8447 8504.06 8280.74 8324.87 8163.6 8178.41 8183.17 8146.52 8331.68 8359.49 8616.21 8711.82 8743.94 8848.15 8915.94 8881.26 9069.29 9093.24 9108.51 9096.72 9070.72 9154.46 9171.61 9286.56 9320.19 9280.97 9256.26 9370.07 9337.95 9241.45 9361.61 9398.19 9321.4 9135.34 9217.94 9279.16 9350.05 9505.96 9509.28 9539.29 9543.52 9580.63 9544.2 9496.28 9310.6 9280.67 9344.61 9441.27 9497.34 9547.22 9627.48 9605.41 9626.8 9683.41 9791.71 9783.92 9820.2 9778.86 9829.87 9748.55 9707.44 9665.19 9789.36 9742.2 9712.28 9509.28 9487.67 9599.75 9731.25 9725.58 9786.87 9864.94 9885.8 9871.06 10015.86 10062.94 9995.91 10092.19 10041.48 9949.36 10081.31 9972.18 9867.96 9882.17 9762.69 9962.58 9712.73 9789.44 9771.91 9802.14 10005.96 10023.42 10226.94 10246.97 10291.26 10197.47 10270.47 10406.96 10437.42 10426.31 10332.44 10318.16 10450.95 10433.71 10464.4 10309.92 10344.84 10471.58 10452.68 10366.15 10388.9 10390.11 10285.97 10337.05 10405.83 10471.5 10501.05 10452 10441.12 10308.26 10328.89 10414.14 10464.93 10466.44 10520.1 10547.08 10545.41 10548.51 10428.05 10583.96 10572.02 10573.68 10606.86 10618.19 10663.99 10627.26 10680.77 10710.55 10609.65 10725.43 10603.15 10389.88 10172.98 10196.86 10194.29 10236.16 10120.46 10067.33 10185.53 10296.85 10270.55 10002.18 10012.23 9908.39 10058.64 10038.38 10144.19 10099.14 10268.81 10309.24 10392.9 10402.35 10383.38 10282.41 10374.16 10321.03 10325.26 10403.79 10405.98 10396.76 10444.14 10566.2 10552.52 10564.38 10567.33 10611.84 10624.69 10642.15 10685.98 10733.67 10779.17 10741.98 10785.89 10888.83 10836.15 10841.21 10850.36 10895.86 10907.42 10856.63 10927.07 10973.55 10969.99 10897.52 10927.07 10997.35 11005.97 11019.42 11123.11 11144.57 11018.66 11092.05 11117.06 11124.92 11134.29 11204.28 11205.03 10991.99 11045.27 11167.32 11008.61 11151.83 10926.77 10868.12 10520.32 10380.43 10785.14 10748.26 10896.91 10782.95 10620.16 10625.83 10510.95 10444.37 10068.01 10193.39 10066.57 10043.75 9974.45 10258.99 10136.63 10024.02 10249.54 10255.28 9931.97 9816.49 9939.98 9899.25 10172.53 10211.07 10190.89 10404.77 10409.46 10434.17 10450.64 10442.41 10293.52 10298.44 10152.8 10143.81 10138.52 9870.3 9774.02 9732.53 9686.48 9743.62 10018.28 10138.99 10198.03 10216.27 10363.02 10366.72 10359.31 10097.9 10154.43 10229.96 10120.53 10322.3 10424.62 10525.43 10537.69 10497.88 10467.16 10465.94 10674.38 10636.38 10680.43 10674.98 10653.56 10698.75 10644.25 10378.83 10319.95 10303.15 10302.01 10405.85 10415.54 10271.21 10213.62 10174.41 10040.45 10060.06 9985.81 10150.65 10009.73 10014.72 10269.47 10320.1 10447.93 10340.69 10387.01 10415.24 10462.77 10544.13 10526.49 10572.73 10594.83 10607.85 10753.62 10761.03 10739.31 10662.42 10860.26 10812.04 10858.14 10835.28 10788.05 10829.68 10751.27 10944.72 10967.65 10948.58 11006.48 11010.34 11020.4 11096.08 11096.92 11062.78 11143.69 10978.62 11107.97 11146.57 11132.56 11164.05 11169.46 11126.28 11113.95 11118.4 11124.62 11188.72 11215.13 11434.84 11444.08 11406.84 11346.75 11357.04 11283.1 11192.58 11201.97 11023.5 11007.88 11181.23 11203.55 11178.58 11036.37 11187.28 11092 11052.49 11006.02 11255.78 11362.41 11382.09 11362.19 11359.16 11372.48 11370.06 11410.32 11428.56 11476.54 11457.47 11499.25 11491.91 11478.13

A noisy signal can be cleaned up by manipulating the signal's Fourier coefficients. In this problem you will explore a few simple approaches where we selectively remove some of the coefficients (these approaches are so-called "filters"). Consider in particular: 1 A"low pass filter" that sets q = 0 ilk > k? 2. A "high pass filter" that setsc,-0 ifkkn 3. A "magnitude filter" that sets c0 if c k? 2. A "high pass filter" that setsc,-0 ifkkn 3. A "magnitude filter" that sets c0 if c