<div dir="ltr"><div>The averaging process is a low-pass filter. A pentad average is a 5-day average. (I assume just a running average.) The frequency response at f=0.2=1/5=(1/N=5) is zero. At frequencies 0.2 to 0.4, the response is negative. Hence, I am not sure what you would be 'band-passing'.<br><br></div>I suggest you use the band-pass on the original daily data. <br><br><br></div><div class="gmail_extra"><br><div class="gmail_quote">On Sun, Dec 25, 2016 at 11:04 PM, Lyndon Mark Olaguera <span dir="ltr"><<a href="mailto:olagueralyndonmark429@gmail.com" target="_blank">olagueralyndonmark429@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><font face="arial, helvetica, sans-serif">Dear all,</font><div><font face="arial, helvetica, sans-serif"><br></font></div><div><font face="arial, helvetica, sans-serif">I have daily interpolated olr data from NOAA (<a href="https://www.esrl.noaa.gov/psd/data/gridded/" target="_blank">https://www.esrl.noaa.gov/<wbr>psd/data/gridded/</a>). I already expressed these data by pentads (73 timesteps). I wanted to do a 20-72 days bandpass filter (butterworth).</font></div><div><font face="arial, helvetica, sans-serif"><br></font></div><div><font face="arial, helvetica, sans-serif">I am confused as to the correct cutoff frequencies should I use and the idea behind this.</font></div><div><font face="arial, helvetica, sans-serif"><br></font></div><div><font face="arial, helvetica, sans-serif">The time step of the data sets is 1 (1 to 73). Is this the correct way of doing this?</font></div><div><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><br></font></span></pre><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><b>fca = dt/t1 = 1./72. (low frequency cutoff)
fcb = dt/t2 = 1./20. (high frequency cutoff)</b></font></span></pre></div><div><div><div class="m_6973907819446992120gmail_signature"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div dir="ltr"><div><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><br></font></span></div><div><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif">Or this:</font></span></div><div><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><b><br></b></font></span></div><div><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><b><span style="color:rgb(0,0,0)">fca = dt/t1 = 5./72. (low frequency cutoff)</span><br></b></font></span></div><div><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><span style="background-color:rgb(255,255,255)"><font face="arial, helvetica, sans-serif"><b>fcb = dt/t2 = 5./20. (high frequency cutoff)</b></font></span></pre><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><font face="arial, helvetica, sans-serif">I hope anyone can help me.<span style="background-color:rgb(255,255,255)"><br></span></font></pre><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><font face="arial, helvetica, sans-serif"><br></font></pre><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><font face="arial, helvetica, sans-serif">Many thanks in advance,</font></pre><pre style="margin-top:0px;margin-bottom:0px;padding:0px;line-height:12pt;border-style:solid;border-width:0px 0px 15px;border-color:transparent;color:rgb(0,0,0)"><font face="arial, helvetica, sans-serif">Lyndon</font></pre></div></div></div></div></div></div></div></div></div>
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