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3. Gather our sample points

Expression 10: "N" equals 512

Expression 11: "p" equals StartFraction, left bracket, 0... left parenthesis, "N" minus 1 , right parenthesis , right bracket Over "N" minus 1 , EndFraction pi

Expression 12: left parenthesis, "p" , "h" Subscript, 2 , Baseline left parenthesis, "p" , right parenthesis , right parenthesis

3. Do a "slow Fourier transform"

Expression 14: "f" Subscript, "D" "C" "T" , Baseline left parenthesis, "k" , "q" , right parenthesis equals "q" left bracket, 1 , right bracket plus "q" left bracket, "N" , right bracket cosine left parenthesis, pi "k" , right parenthesis plus 2 Start sum from "n" equals 1 to "N" minus 2, end sum, "q" left bracket, "n" plus 1 , right bracket cosine left parenthesis, StartFraction, pi Over "N" minus 1 , EndFraction "n" "k" , right parenthesis

Expression 15: "X" equals "f" Subscript, "D" "C" "T" , Baseline left parenthesis, left bracket, 0... "N" minus 1 , right bracket , "h" Subscript, 2 , Baseline left parenthesis, "p" , right parenthesis , right parenthesis

Expression 16: "y" equals StartFraction, "f" Subscript, "D" "C" "T" , Baseline left parenthesis, StartNestedFraction, "N" minus 1 NestedOver pi , EndNestedFraction "x" , "X" , right parenthesis Over 2 left parenthesis, "N" minus 1 , right parenthesis , EndFraction

4. It actually looks alright! But in terms of worst-case error, it's pretty off near zero

Expression 18: absolute value left parenthesis, StartFraction, "f" Subscript, "D" "C" "T" , Baseline left parenthesis, StartNestedFraction, "N" minus 1 NestedOver pi , EndNestedFraction "x" , "X" , right parenthesis Over 2 left parenthesis, "N" minus 1 , right parenthesis , EndFraction minus "h" Subscript, 2 , Baseline left parenthesis, "x" , right parenthesis , right parenthesis

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