I have a sequence of 12 numbers t1 to t12 which I analysed using FFT to denoise as shown in the image which gave me 2 unique values a&b.sequence 1979,156,1338,1004,1433,672,555,1451,1703,452,1171,815,FFT gave me a=1363,b=758.So,I was able to derive the rest given a, b, t7, t10.