diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..45db154
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,1021 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.9.4"
+manifest_format = "2.0"
+project_hash = "82f88ffebcb2d410dac15f0e84acb433b08e60da"
+
+[[deps.AbstractFFTs]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "d92ad398961a3ed262d8bf04a1a2b8340f915fef"
+uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+version = "1.5.0"
+weakdeps = ["ChainRulesCore", "Test"]
+
+    [deps.AbstractFFTs.extensions]
+    AbstractFFTsChainRulesCoreExt = "ChainRulesCore"
+    AbstractFFTsTestExt = "Test"
+
+[[deps.AliasTables]]
+deps = ["PtrArrays", "Random"]
+git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
+uuid = "66dad0bd-aa9a-41b7-9441-69ab47430ed8"
+version = "1.1.3"
+
+[[deps.ArgTools]]
+uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
+version = "1.1.1"
+
+[[deps.Artifacts]]
+uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
+
+[[deps.AxisAlgorithms]]
+deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
+git-tree-sha1 = "66771c8d21c8ff5e3a93379480a2307ac36863f7"
+uuid = "13072b0f-2c55-5437-9ae7-d433b7a33950"
+version = "1.0.1"
+
+[[deps.Base64]]
+uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
+
+[[deps.Blosc_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Lz4_jll", "Zlib_jll", "Zstd_jll"]
+git-tree-sha1 = "19b98ee7e3db3b4eff74c5c9c72bf32144e24f10"
+uuid = "0b7ba130-8d10-5ba8-a3d6-c5182647fed9"
+version = "1.21.5+0"
+
+[[deps.BufferedStreams]]
+git-tree-sha1 = "6863c5b7fc997eadcabdbaf6c5f201dc30032643"
+uuid = "e1450e63-4bb3-523b-b2a4-4ffa8c0fd77d"
+version = "1.2.2"
+
+[[deps.Bzip2_jll]]
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "9e2a6b69137e6969bab0152632dcb3bc108c8bdd"
+uuid = "6e34b625-4abd-537c-b88f-471c36dfa7a0"
+version = "1.0.8+1"
+
+[[deps.CSV]]
+deps = ["CodecZlib", "Dates", "FilePathsBase", "InlineStrings", "Mmap", "Parsers", "PooledArrays", "PrecompileTools", "SentinelArrays", "Tables", "Unicode", "WeakRefStrings", "WorkerUtilities"]
+git-tree-sha1 = "6c834533dc1fabd820c1db03c839bf97e45a3fab"
+uuid = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
+version = "0.10.14"
+
+[[deps.Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
+
+[[deps.CatViews]]
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+git-tree-sha1 = "23d1f1e10d4e24374112fcf800ac981d14a54b24"
+uuid = "81a5f4ea-a946-549a-aa7e-2a7f63a27d31"
+version = "1.0.0"
+
+[[deps.ChainRulesCore]]
+deps = ["Compat", "LinearAlgebra"]
+git-tree-sha1 = "71acdbf594aab5bbb2cec89b208c41b4c411e49f"
+uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+version = "1.24.0"
+weakdeps = ["SparseArrays"]
+
+    [deps.ChainRulesCore.extensions]
+    ChainRulesCoreSparseArraysExt = "SparseArrays"
+
+[[deps.ClimateModels]]
+deps = ["CSV", "DataFrames", "Dates", "Downloads", "Git", "OrderedCollections", "Pkg", "Statistics", "Suppressor", "TOML", "Test", "UUIDs"]
+git-tree-sha1 = "c15e03226f2b3c65b84d2e7d61d7d67e9dca0868"
+uuid = "f6adb021-9183-4f40-84dc-8cea6f651bb0"
+version = "0.3.5"
+
+    [deps.ClimateModels.extensions]
+    ClimateModelsCondaExt = ["Conda"]
+    ClimateModelsMakieExt = ["Makie"]
+    ClimateModelsPyCallExt = ["PyCall"]
+
+    [deps.ClimateModels.weakdeps]
+    Conda = "8f4d0f93-b110-5947-807f-2305c1781a2d"
+    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+    PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+
+[[deps.CodeTracking]]
+deps = ["InteractiveUtils", "UUIDs"]
+git-tree-sha1 = "7eee164f122511d3e4e1ebadb7956939ea7e1c77"
+uuid = "da1fd8a2-8d9e-5ec2-8556-3022fb5608a2"
+version = "1.3.6"
+
+[[deps.CodecZlib]]
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+git-tree-sha1 = "b8fe8546d52ca154ac556809e10c75e6e7430ac8"
+uuid = "944b1d66-785c-5afd-91f1-9de20f533193"
+version = "0.7.5"
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+[[deps.Compat]]
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+weakdeps = ["Dates", "LinearAlgebra"]
+
+    [deps.Compat.extensions]
+    CompatLinearAlgebraExt = "LinearAlgebra"
+
+[[deps.CompilerSupportLibraries_jll]]
+deps = ["Artifacts", "Libdl"]
+uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
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+[[deps.Crayons]]
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+
+[[deps.DataAPI]]
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+
+[[deps.DataFrames]]
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+git-tree-sha1 = "04c738083f29f86e62c8afc341f0967d8717bdb8"
+uuid = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
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+[[deps.DataStructures]]
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+[[deps.DataValueInterfaces]]
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+[[deps.Dates]]
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+[[deps.DelimitedFiles]]
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+[[deps.Dierckx]]
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+[[deps.Dierckx_jll]]
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+[[deps.Distances]]
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+weakdeps = ["ChainRulesCore", "SparseArrays"]
+
+    [deps.Distances.extensions]
+    DistancesChainRulesCoreExt = "ChainRulesCore"
+    DistancesSparseArraysExt = "SparseArrays"
+
+[[deps.Distributed]]
+deps = ["Random", "Serialization", "Sockets"]
+uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
+
+[[deps.Distributions]]
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+    [deps.Distributions.extensions]
+    DistributionsChainRulesCoreExt = "ChainRulesCore"
+    DistributionsDensityInterfaceExt = "DensityInterface"
+    DistributionsTestExt = "Test"
+
+    [deps.Distributions.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    DensityInterface = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[deps.DocStringExtensions]]
+deps = ["LibGit2"]
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+[[deps.Downloads]]
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+    FillArraysSparseArraysExt = "SparseArrays"
+    FillArraysStatisticsExt = "Statistics"
+
+[[deps.FortranFiles]]
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+    [deps.HDF5.weakdeps]
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+[[deps.HDF5_jll]]
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+    [deps.InlineStrings.weakdeps]
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+[[deps.LaTeXStrings]]
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diff --git a/src/ECCOtour.jl b/src/ECCOtour.jl
index 378e704..a031cb9 100644
--- a/src/ECCOtour.jl
+++ b/src/ECCOtour.jl
@@ -14,7 +14,7 @@ import Statistics.mean, Statistics.std,
 
 export hanncoeffs, hannsum, hannsum!, hannfilter
 export get_filtermatrix, matrixfilter, matrixspray, columnscale!
-export seasonal_matrices, trend_matrices
+export seasonal_matrices, trend_matrices, mean_matrices
 export position_label, searchdir
 export listexperiments, expnames, expsymbols, time_label
 export inrectangle, isnino34, issouthpac, isnino3, isnino4, isnino12
diff --git a/src/SeasonalCycle.jl b/src/SeasonalCycle.jl
index bbf04b2..fd0342f 100644
--- a/src/SeasonalCycle.jl
+++ b/src/SeasonalCycle.jl
@@ -8,7 +8,7 @@
 - `E`: matrix that solves E*parameters= seasonal cycle
 - `F=E†`: generalized inverse of `E`
 """
-function seasonal_matrices(fcycle,t,overtones=1)
+function seasonal_matrices(fcycle,t,overtones=1, fit_mean = true)
 
     ω = 2π * fcycle # day^{-1} , seasonal frequency
     nt = length(t)
@@ -31,6 +31,11 @@ function seasonal_matrices(fcycle,t,overtones=1)
         E[:,i+freqs+1] = cos.(i*ω*t)
     end
 
+    # If mean is not fitted, remove the first column
+    if !fit_mean
+        E = E[:, 2:end]
+    end
+
     F = (E'*E)\E' # least squares estimator
 
     return E,F
@@ -67,3 +72,24 @@ function trend_matrices(t)
 end
 
 
+"""
+    function mean_matrices(t)
+        
+    computes the mean using matrix inversions
+# Arguments
+- `t`: time
+# Output
+- `E`: matrix that solves E*parameters= timeseries
+- `F=E†`: generalized inverse of `E`
+"""
+function mean_matrices(t)
+    nt = length(t)
+
+    # Create the matrix E for fitting the mean
+    E = ones(Float32, nt, 1)
+    println(size(E))
+
+    F = (E' * E) \ E' # least squares estimator
+
+    return E, F
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index d45a333..b621f9e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -32,7 +32,9 @@ using Downloads
     @testset "basin mask" begin
         include(testdir("test_basinmask.jl"))
     end
-
+    @testset "SeasonalCycle" begin
+        include(testdir("test_seasonalcycle.jl"))
+    end
     cd(srcdir())
     # workaround: use a shell script
     #run(`sh $srcdir/download_google_drive.sh`)
diff --git a/test/test_seasonalcycle.jl b/test/test_seasonalcycle.jl
new file mode 100644
index 0000000..1232670
--- /dev/null
+++ b/test/test_seasonalcycle.jl
@@ -0,0 +1,27 @@
+# Define test parameters
+fcycle = 1.0 / 365.0
+t = 1:365  # One year of daily data
+overtones = 2
+
+# Test fit_mean function
+E_mean, F_mean = mean_matrices(t)
+@test size(E_mean) == (365, 1)
+@test all(E_mean[:, 1] .== 1.0)
+
+# Test seasonal_matrices with fit_mean = true
+E1, F1 = seasonal_matrices(fcycle, t, overtones, true)
+@test size(E1) == (365, (overtones + 1) * 2 + 1)
+@test all(E1[:, 1] .== 1.0)
+
+# Test seasonal_matrices with fit_mean = false
+E2, F2 = seasonal_matrices(fcycle, t, overtones, false)
+@test size(E2) == (365, (overtones + 1) * 2)
+
+# Check that the sine and cosine values are correctly computed
+ω = 2π * fcycle
+for i = 1:overtones+1
+    @test all(E1[:, i+1] .≈ sin.(i * ω * t))
+    @test all(E1[:, i+overtones+2] .≈ cos.(i * ω * t))
+    @test all(E2[:, i] .≈ sin.(i * ω * t))
+    @test all(E2[:, i+overtones+1] .≈ cos.(i * ω * t))
+end
\ No newline at end of file